HP Prime Graphing Wireless Calculator User Manual

HP Prime Graphing Calculator

User Guide Supplement

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© Copyright 2014 Hewlett-Packard Development Company, L.P. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws. First Edition: April 2014 Document Part Number: 775775-001

About this guide

The information in this guide updates the information in the following chapters of the HP Prime Calculator User Guide:

•Geometry

•Inference app

• Functions and commands

• Variables

• Programming in HP PPL

If there is a conflict between the information in these guides, use the information provided in this guide.

1Geometry

Getting started with the Geometry app ...................................... 5

Plot view in detail.................................................................. 12

The Options menu ............................................................ 17

Plot Setup view................................................................. 18

Symbolic view in detail.......................................................... 19

Symbolic Setup view......................................................... 20

Numeric view in detail .......................................................... 20

Plot view: Cmds menu ........................................................... 23

Geometry functions and commands......................................... 39

Symbolic view: Cmds menu ............................................... 40

Numeric view: Cmds menu................................................ 55

Other Geometry functions.................................................. 60

2 Inference app

Getting started with the Inference app ..................................... 70

Importing statistics................................................................. 74

Hypothesis tests .................................................................... 77

One-Sample Z-Test............................................................ 77

Two-Sample Z-Test ............................................................ 78

One-Proportion Z-Test........................................................ 79

Two-Proportion Z-Test ........................................................ 80

One-Sample T-Test ............................................................ 81

Two-Sample T-Test ............................................................ 82

Confidence intervals.............................................................. 84

One-Sample Z-Interval....................................................... 84

Two-Sample Z-Interval ....................................................... 84

One-Proportion Z-Interval................................................... 85

Two-Proportion Z-Interval ................................................... 86

One-Sample T-Interval ....................................................... 87

Two-Sample T-Interval........................................................ 87

Chi-square tests..................................................................... 88

Goodness of fit test ........................................................... 88

Two-way table test ............................................................ 89

Inference for regression ......................................................... 90

Linear t-test ...................................................................... 91

Confidence interval for slope ............................................. 92

Confidence interval for intercept......................................... 94

Confidence interval for a mean response............................. 95

Prediction interval............................................................. 96

Contents 1

3 Functions and commands

Keyboard functions..............................................................101

Math menu ......................................................................... 105

Numbers........................................................................ 105

Arithmetic ......................................................................106

Trigonometry .................................................................. 108

Hyperbolic.....................................................................109

Probability .....................................................................109

List ................................................................................114

Matrix ...........................................................................115

Special .......................................................................... 115

CAS menu ..........................................................................116

Algebra.........................................................................116

Calculus ........................................................................ 118

Solve............................................................................. 122

Rewrite ..........................................................................124

Integer........................................................................... 129

Polynomial ..................................................................... 131

Plot ...............................................................................138

App menu ..........................................................................138

Function app functions..................................................... 139

Solve app functions......................................................... 140

Spreadsheet app functions ...............................................140

Statistics 1Var app functions............................................. 154

Statistics 2Var app functions............................................. 156

Inference app functions....................................................157

Finance app functions .....................................................166

Linear Solver app functions .............................................. 168

Triangle Solver app functions ...........................................168

Linear Explorer functions .................................................. 170

Quadratic Explorer functions ............................................ 171

Common app functions....................................................171

Ctlg menu........................................................................... 172

Creating your own functions ................................................. 213

4 Variables

Qualifying variables ............................................................ 219

Home variables...................................................................220

App variables ..................................................................... 221

Function app variables ....................................................221

Geometry app variables ..................................................222

Spreadsheet app variables............................................... 223

Solve app variables ........................................................223

Advanced Graphing app variables ...................................224

2 Contents

Statistics 1Var app variables............................................ 225

Statistics 2Var app variables............................................ 227

Inference app variables................................................... 229

Parametric app variables................................................. 233

Polar app variables ........................................................ 234

Finance app variables..................................................... 234

Linear Solver app variables ............................................. 235

Triangle Solver app variables .......................................... 235

Linear Explorer app variables .......................................... 235

Quadratic Explorer app variables .................................... 235

Trig Explorer app variables ............................................. 236

Sequence app variables.................................................. 236

5 Programming in HP PPL

The Program Catalog .......................................................... 238

Creating a new program ..................................................... 241

The Program Editor ......................................................... 242

The HP Prime programming language ................................... 251

The User Keyboard: Customizing key presses .................... 256

App programs ............................................................... 260

Program commands ............................................................ 267

Commands under the Tmplt menu..................................... 268

Block ............................................................................ 268

Branch .......................................................................... 268

Loop ............................................................................. 269

Variable........................................................................ 273

Function ........................................................................ 273

Commands under the Cmds menu .................................... 274

Strings .......................................................................... 274

Drawing........................................................................ 277

Matrix........................................................................... 289

App Functions ................................................................ 290

Integer .......................................................................... 292

I/O .............................................................................. 294

More ............................................................................ 299

Variables and Programs .................................................. 301

Index ................................................................................... 327

Contents 3

4 Contents

Geometry

The Geometry app enables you to draw and explore geometric constructions. A geometric construction can be composed of any number of geometric objects, such as points, lines, polygons, curves, tangents, and so on. You can take measurements (such as areas and distances), manipulate objects, and note how measurements change.

There are five app views:

• Plot view: provides drawing tools for you to construct geometric objects

• Symbolic view: provides editable definitions of the objects in Plot view

• Numeric view: for making calculations about the objects in Plot view

• Plot Setup view: for customizing the appearance of Plot view

• Symbolic Setup view: for overriding certain system-wide settings

There is no Numeric Setup view in this app.

To open the Geometry app, press

Geometry. The app opens in Plot view.

I and select

Getting started with the Geometry app

The following example shows how you can graphically represent the derivative of a curve, and have the value of the derivative automatically update as you move a point of tangency along the curve. The curve to be explored is y = 3sin(x).

Since the accuracy of our calculation in this example is not too important, we will first change the number format to fixed at 3 decimal places. This will also help keep our geometry workspace uncluttered.

Geometry 5

Preparation 1. P r e s s SK.

2. On the first CAS settings page, set the number format to Standard and the number of decimal places to 4.

Open the app and plot the graph

3. Press I and select Geometry.

If there are objects showing that you don’t need, press

SJ and confirm your intention by tapping .

The app opens in Plot view. This view displays a Cartesian plane with a menu bar at the bottom. Next to the menu bar, this view displays the coordinates of the cursor. After you interact with the app, the bottom of the display displays the currently active tool or command, help for the current tool or command, and a list of all objects recognized as being under the current pointer location.

4. Select the type of graph you want to plot. In this example we are plotting a simple sinusoidal function, so choose:

> Plot > Function

5. With plotfunc( on the entry line, enter 3*sin(x):

seASsE

Note that x must be entered in lowercase in the Geometry app.

If your graph doesn’t resemble the illustration at the right, adjust the

Rng

and Y Rng values in Plot Setup view (

SP).

We’ll now add a point to the curve, a point that will be constrained always to follow the contour of the curve.

Add a constrained point

6 Geometry

6. Tap , tap Point, and then select Point On.

Choosing Point On rather than Point means that the point will be constrained to whatever it is placed on.

7. Ta p a ny wh ere on th e graph, press and then press

Notice that a point is added to the graph and given a name (B in this example). Tap a blank area of the screen to deselect everything. (Objects colored light blue are selected.)

Add a tangent 8. We will now add a tangent to the curve, making point B

the point of tangency:

> Line > Tangent

9. When prompted to select a curve, tap anywhere on the curve and press When prompted to select a point, tap point B and press see the tangent. Press

E to

J to close the Tangent tool.

Depending on where you placed point B, your illustration might be different from the one at the right. Now, make the tangent stand out by giving it a bright color.

10. Tap on the tangent to select it. After the tangent is selected, the new menu key appears. Tap or press Z, and then select Choose color.

11. Pick a color, and then tap on a blank area of the screen to see the new color of the tangent line.

12. Ta p p oin t B and drag it along the curve; the tangent moves accordingly. You can also drag the tangent line itself.

13. Ta p po in t B and then press The point turns light blue to show that it has been selected. Now, you can either drag the point with your finger or use the cursor keys for finer control of the

E to select the point.

Geometry 7

movement of point B. To deselect point B, either press J or tap point B and press

Note that whatever you do, point B remains constrained to the curve. Moreover, as you move point B, the tangent moves as well. If it moves off the screen, you can bring it back by dragging your finger across the screen in the appropriate direction.

Create a derivative point

The derivative of a graph at any point is the slope of its tangent at that point. We’ll now create a new point that will be constrained to point B and whose ordinate value is the derivative of the graph at point B. We’ll constrain it by forcing its x coordinate (that is, its abscissa) to always match that of point B, and its y coordinate (that is, its ordinate) to always equal the slope of the tangent at that point.

14. To define a point in terms of the attributes of other geometric objects, you need to go to Symbolic view:

Note that each object you have so far created is listed in Symbolic view. Note too that the name for an object in Symbolic view is the name it was given in Plot view but prefixed with a “G”. Thus the graph—labeled A in Plot view—is labeled GA in Symbolic view.

15. Highlight the blank definition following GC and tap

When creating objects that are dependent on other objects, the order in which they appear in Symbolic view is important. Objects are drawn in Plot view in the order in which they appear in Symbolic view. Since we are about to create a new point that is dependent on the attributes of GB and GC, it is important that we place its definition after that of both GB and GC. That is why we made sure we were at the bottom the list of definitions before tapping . If the new definition appeared higher up in Symbolic view, the point created in the following step would not be active in Plot view.

8 Geometry

16. T a p a n d c h oos e Point > point

You now need to specify the x and y coordinates of the new point. The former is defined as the abscissa of point B (referred to as GB in Symbolic view) and the latter is defined as the slope of tangent line C (referred to as GC in Symbolic view).

17. Yo u sh o ul d ha v e point() on the entry line. Between the parentheses, add:

abscissa(GB),slope(GC)

For the abscissa command, tap , select Cartesian, and then select abscissa. For the slope command, tap

, select Measure, and then select slope.

18. Ta p .

The definition of your new point is added to Symbolic view. When you return to Plot view, you will see a point named D and it will have the same x- coordinate as point B.

19. Press

If you can’t see point D, pan until it comes into view. The y coordinate of D will be the derivative of the curve at point B.

Since it is difficult to read coordinates off the screen, we’ll add a calculation that will give the exact derivative (to three decimal places) and which we can display in Plot view.

Add some calculations

Geometry 9

20.Press M.

Numeric view is where you enter calculations.

21. Ta p .

22. Tap and choose Measure > slope

23. Between parentheses, add the name of the tangent, namely GC, and tap .

Notice that the current slope is calculated and displayed. The value here is dynamic, that is, if the slope of the tangent changes in Plot view, the value of the slope is automatically updated in Numeric view.

24.With the new calculation highlighted in Numeric view, tap .

Selecting a calculation in Numeric view means that it will also be displayed in Plot view.

25. Press

26. Press

27. Tap the last blank field to select it, and then tap to

28.To start a third calculation, tap , select

29. Make sure both of these new equations are selected (by

30.Press

P to return to

Plot view.

Notice the calculation that you have just created in Numeric view is displayed at the top left of the screen.

Let’s now add two more calculations to Numeric view and have them displayed in Plot view.

M to return to Numeric view.

start a new calculation. Tap , select Cartesian, and then select Coordinates. Between the parentheses, enter GB and then tap .

Cartesian, and then select Equation of. Between the parentheses, enter GC and then tap .

choosing each one and pressing ).

P to return to

Plot view.

Notice that your new calculations are displayed.

10 Geometry

31. Ta p p oi n t B and then press E to select it.

32.Use the cursor keys to move point B along the graph. Note that with each move, the results of the calculations shown at the top left of the screen change. To deselect point B, tap point B and then press

Calculations in Plot view

Trace the derivative

By default, calculations in Plot view are docked to the upper left of the screen. You can drag a calculation from its dock and position it anywhere you like; however, after being undocked, the calculation scrolls with the display. Tap and hold a calculation to edit its label. An edit line opens so that you can enter your own label. You can also tap and select a different color for the calculation and its label. Tap when you are done.

Point D is the point whose ordinate value matches the derivative of the curve at point B. It is easier to see how the derivative changes by looking at a plot of it rather than comparing subsequent calculations. We can do that by tracing point D as it moves in response to movements of point B.

First we’ll hide the calculations so that we can better see the trace curve.

33. Press

34.Select each calculation in turn and tap . All

35. Press

36. Tap point D and then press E to select it.

37. Tap (or press Z) and then select Trace. Press

M to return to Numeric view.

calculations should now be deselected.

P to return to Plot view.

E to deselect point D.

38.Tap point B and then press

39. Using the cursor keys, move point B along the curve. Notice that a shadow curve is traced out as you move point B. This is the curve of the

E to select it.

Geometry 11

derivative of 3sin(x). Tap point B and then press E to deselect it.

Plot view in detail

In Plot view you can directly draw objects on the screen using various drawing tools. For example, to draw a circle, tap , tap

Curve, and then select Circle. Now, tap where

you want the center of the circle to be and press on the circumference and press with a center at the location of your first tap, and with a radius equal to the distance between your first tap and second tap.

Note that there are on-screen instructions to help you. These instructions appear near the bottom of the screen, next to the command listing for the active tool (circle, point, and so on).

You can draw any number of geometric objects in Plot view. See “Plot view: Cmds menu” on page 23 for a list of the objects you can draw. The drawing tool you choose—line, circle, hexagon, and so on—remains selected until you deselect it. This enables you to quickly draw a number of objects of the same type (such as a number of hexagons). After you have finished drawing objects of a particular type, deselect the drawing tool by pressing drawing tool is still active by the presence of the on-screen instructions and the command name at the bottom of the screen.

An object in Plot view can be manipulated in numerous ways, and its mathematical properties can be easily determined (see page 20).

E. Next, tap a point that is to be

E. A circle is drawn

J. You can tell if a

Selecting objects Selecting an object involves at least two steps: tapping the

object and pressing to confirm your intention to select an object.

When you tap a location, objects recognized as being under the pointer are colored light red and added to the list of

12 Geometry

E. Pressing E is necessary

objects in the bottom right corner of the display. You can select any or all of these objects by pressing tap the screen and then use the cursor keys to accurately position the pointer before pressing

When more tha n one object is recognized as b eing under t he pointer, in most cases, preference is given to any point under the pointer when up box appears enabling you to select the desired objects.

You can also select multiple objects using a selection box. Tap and hold your finger at the location on the screen that represents one corner of the selection rectangle. Then drag your finger to the opposite corner of the selection rectangle. A light blue selection rectangle is drawn as you drag. Objects that touch this rectangle are selected.

E is pressed. In other cases, a pop-

E. You can

Hiding names You can choose to hide the name of an object in Plot view:

1. Select the object whose label you want to hide.

2. Tap or press

3. Select Hide Label.

Redisplay a hidden name by repeating this procedure and selecting Show Label.

Moving objects There are many ways to m ove objects. First, to move a n object

quickly, you can drag the object without selecting it.

Second, you can tap an object and press Then, you can drag the object to move it quickly or use the cursor keys to move it one pixel at a time. With the second method, you can select multiple objects to move together. When you have finished moving objects, tap a location where there are no objects and press If you have selected a single object, you can tap the object and press

Third, you can move a point on an object. Each point on an object has a calculation labeled with its name in Plot view. Tap and hold this item to display a slider bar. You can drag the slider or use the cursor keys to move it. appears as a new menu key. Tap this key to display a dialog box where you can specify the start, step, and stop values for the slider. Also, you can create an animation based on this point using

E to deselect it.

E to deselect everything.

E to select it.

Geometry 13

the slider. You can set the speed and pause for the animation, as well as its type. To start or stop an animation, select it, tap

, and then select or clear the Animate option.

Coloring objects Objects are colored black by default. The procedure to

change the color of an object depends on which view you are in. In both the Symbolic and Numeric view, each item includes a set of color icons. Tap these icons and select a color. In Plot view, select the object, tap (or press Z), tap Choose Color, and then select a color.

Filling objects An object with closed contours (such as a circle or polygon)

can be filled with color.

1. Se l e c t t h e o b je ct .

2. Tap or press Z.

3. Select Filled.

Filled is a toggle. To remove a fill, repeat the above procedure.

Clearing an object

14 Geometry

To clear one object, select it and tap C. Note that an object is distinct from the points you entered to create it. Thus deleting the object does not delete the points that define it. Those points remain in the app. For example, if you select a circle and press and radius point remain.

If other objects are dependent on the one you have selected for deletion, a pop-up displays the selected object and all dependent objects checked for deletion. Confirm your intention by tapping .

You can select multiple items for deletion. Either select them one at a time or use a selection box, and then press C.

Note that points you add to an object once the object has been defined are cleared when you clear the object. Thus if you place a point (say D) on a circle and delete the circle, the

C, the circle is deleted but the center point

circle and D are deleted, but the defining points—the center and radius points—remain.

Clearing all objects

Gestures in Plot view

To clear the app of all geometric objects, press SJ. You will be asked to confirm your intention to do so. Tap to clear all objects defined in Symbolic view or to keep the app as it is. You can clear all measurements and calculations in Numeric view in the same way.

You can pan by dragging a finger across the screen: either up, down, left, or right. You can also use the cursor keys to pan once the cursor is at the edge of the screen. You can use a pinch gesture to zoom in or out. Place two fingers on the screen. Move them apart to zoom in or bring them together to zoom out. You can also press + to zoom in on the pointer or press w to zoom out on the pointer.

Zooming You can zoom by tapping and choosing a zoom

option. The zoom options are the same as you find in the Plot view of many apps in the calculator.

Geometry 15

Plot view: buttons and keys

Button or key Purpose

Opens the Commands menu. See “Plot view: Cmds menu” on page 23.

Opens the Options menu for the selected object.

Hides (or displays) the axes.

J SJ

Selects the circle drawing tool. Follow the instructions on the screen (or see page

28). Erases all trace lines.

Selects the intersection drawing tool. Follow the instructions on the screen (or see page 24).

Selects the line drawing tool. Follow the instructions on the screen (or see page

25). Selects the point drawing tool. Follow the

instructions on the screen (or see page

24) . Selects the segment drawing tool. Follow

the instructions on the screen (or see page

25). Selects the triangle drawing tool. Follow

the instructions on the screen (or see page

26) . Deletes a selected object (or the character

to the left of the cursor if the entry line is active).

Deselects the current drawing tool.

Clears the Plot view of all geometric objects or the Numeric view of all measurements and calculations.

16 Geometry

The Options menu

When you select an object, a new menu key appears:

object, such as color. The Options menu changes depending on the type of object selected. The complete set of Geometry options are listed in the following table and are also displayed when you press Z.

. Tap this key to view and select options for the selected

Option

Choose Color

Hide

Hide Label

Filled

Trace

Clear Trace

Animate

Purpose

Displays a set of color icons so you can select a color for the selected object.

Hides the selected object. This is a shortcut for deselecting the object in Symbolic view. To select an object to display after it has been hidden, go to Symbolic or Numeric view.

Hides the label of a selected object. This option changes to Show Label if the selected object has a hidden label.

Fills the selected object with a color. Clear this option to remove the fill.

Starts tracing for any selected point if selected, then stops tracing for the selected point.

Erases the current trace of the selected point but does not stop tracing.

Starts the current animation of a selected point on an object. If the selected point is currently animated, this option stops the animation.

Geometry 17

Plot Setup view

The Plot Setup view enables you to configure the appearance of Plot view.

The fields and options are as follows:

•

X Rng: There are two

boxes, but only the minimum x-value is editable. The maximum x-value is calculated automatically, based on the minimum value and the pixel size. You can also change the x range by panning and zooming in Plot view.

•

Y Rng: There are two boxes, but only the minimum y-

value is editable. The maximum y-value is calculated automatically, based on the minimum value and the pixel size. You can also change the y range by panning and zooming in Plot view.

• Pixel Size: Each pixel in the Plot view must be square.

You can change the size of each pixel. The lower left corner of the Plot view display remains the same, but the upper right-corner coordinates are automatically recalculated.

•

Axes: A toggle option to hide (or show) the axes in Plot

view.

Keyboard shortcut:

• Labels: A toggle option to hide (or show) the labels for the axes.

•

Grid Dots: A toggle option to hide (or show) the grid

dots.

• Grid Lines: A toggle option to hide (or show) the grid lines.

18 Geometry

Symbolic view in detail

Every object—whether a point, segment, line, polygon, or curve—is given a name, and its definition is displayed in Symbolic view (

Y). The name is the

name for it you see in Plot view, but prefixed by “G”. Thus a point labeled A in Plot view is given the name GA in Symbolic view.

The G-prefixed name is a variable that can be read by the computer algebra system (CAS). Thus in the CAS you can include such variables in calculations. Note in the illustration above that GC is the name of the variable that represents a circle drawn in Plot view. If you are working in the CAS and wa nted to know what the are a of that ci rcle is, you c ould enter area(GC) and press

Note

Calculations referencing geometry variables can be made in the CAS or in the Numeric view of the Geometry app (explained below on page 20).

You can change the definition of an object by selecting it, tapping , and altering one or more of its defining parameters. The object is modified accordingly in Plot view. For example, if you selected point GB in the illustration above, tapped , changed one or both of the point’s coordinates, and tapped , you would find, on returning to Plot view, a circle of a different size.

Creating objects You can also create an object in Symbolic view. Tap ,

define the object—for example, point(4,6)—and press

E. The object is created and can be seen in Plot view.

Another example: to draw a line through points P and Q, enter line(GP,GQ) in Symbolic view and press When you return to Plot view, you will see a line passing through points P and Q.

Geometry 19

The object-creation commands available in Symbolic view can be seen by tapping . The syntax for each command is given in “Geometry functions and commands” on page 39.

Re-ordering entries

You can re-order the entries in Symbolic view. Objects are drawn in Plot view in the order in which they are defined in Symbolic view. To change the position of an entry, highlight it and tap either (to move it down the list) or (to move it up).

Hiding an object To prevent an object displaying in Plot view, deselect it in

Symbolic view:

1. Highlight the item to be hidden.

2. Tap .

Repeat the procedure to make the object visible again.

Deleting an object

As well as deleting an object in Plot view (see page 14) you can delete an object in Symbolic view.

1. Highlight the definition of the object you want to delete.

2. Press

To delete all objects, press

SJ. When prompted, tap

to confirm the deletion.

Symbolic Setup view

The Symbolic view of the Geometry app is common with many apps. It is used to override certain system-wide settings.

Numeric view in detail

Numeric view (M) enables you to do calculations in the Geometry app. The results displayed are dynamic—if you manipulate an object in Plot view or Symbolic view, any calculations in Numeric view that refer to that object are

20 Geometry

automatically updated to reflect the new properties of that object.

Consider circle C in the illustration at the right. To calculate the area and radius of C:

1. Press

2. Tap .

3. Tap and choose

4. Tap , choose Curves and then the curve whose

5. Press

6. Tap .

7. E n t e r radius(GC) and

M to open

Numeric view.

Measure > Area.

Note that area() appears on the entry line, ready for you to specify the object whose area you are interested in.

area you are interested in.

The name of the object is placed between the parentheses.

You could have entered the command and object name manually, that is, without choosing them from menus. If you enter object names manually, remember that the name of the object in Plot view must be given a “G” prefix if it is used in any calculation. Thus the circle named C in Plot view must be referred to as GC in Numeric view and Symbolic view.

E or tap . The area is displayed.

tap . The radius is displayed. Use to verify both of these measurements so that they will be available in Plot view.

Geometry 21

Note

Note that the syntax used here is the same as you use in the CAS to calculate the properties of geometric objects.

The Geometry functions and their syntax are described in “Geometry functions and commands” on page 39.

8. Press

If an entry in Numeric view is too long for the screen, you can press > to scroll the rest of the entry into view. Press < to scroll back to the original view.

P to go back to Plot view. Now, manipulate the

circle in some way that changes its area and radius. For example, select the center point (A) and use the cursor keys to move it to a new location. Notice that the area and radius calculations update automatically as you move the point. Remember to press J finished.

when you are

Listing all objects

Displaying calculations in Plot view

When you are creating a new calculation in Numeric view, the menu item appears. Tapping gives you a list of all the objects in your Geometry workspace.

If you are building a calculation, you can select an object’s vari able na me from this menu. The name of the selected object is placed at the insertion point on the entry line.

To have a calculation made in Numeric view appear in Plot view, just highlight it in Numeric view and tap

. A checkmark appears beside the calculation.

Repeat the procedure to prevent the calculation being displayed in Plot view. The checkmark is cleared.

22 Geometry

Editing a calculation

1. Highlight the calculation that you want to edit.

2. Tap to change the calculation or tap to change the label.

3. Make your changes and tap .

Deleting a calculation

1. Highlight the calculation you want to delete.

2. Press C.

To delete all calculations, press a calculation does not delete any geometric objects from either the Plot or Symbolic view.

Plot view: Cmds menu

The geometric objects discussed in this section are those that can be created in either Plot view or Symbolic view using the Commands menu ( ). This section discusses how to use the commands in Plot view. Objects can also be created in Symbolic view—more, in fact, than in Plot view—but these are discussed in “Geometry functions and commands” on page 39. Finally, measurements and other calculations can be performed in Plot view as well.

In Plot view, you ch oose a drawing tool to draw an object. The tools are listed in this section. Note that once you select a drawing tool, it remains selected until you deselect it. This enables you to quickly draw a number of objects of the same type (such as a number of circles). To deselect the current drawing tool, press active by the presence of the on-screen help in the bottom leftside of the screen and the current command statement to its right.

The steps provided in this section are based on touch entry. For example, to add a point, the steps will tell you to tap on the screen where you want the point to be and press However, you can also use the cursor keys to position the cursor where you want the point to be and then press

The drawing tools for the geometric objects listed in this section can be selected from the Commands menu at the bottom of the screen ( ). Some objects can also be

SJ. Note that deleting

J. You can tell if a drawing tool is still

Geometry 23

entered using a keyboard shortcut. For example, you can select the triangle drawing tool by pressing view: buttons and keys” on page 16.

n. See “Plot

Point Tap to display a menu and submenus of options for

entering various types of points. The menus and submenus are:

Point Tap where you want the point to be and press

Keyboard shortcut: B

Point On Tap the object where you want the new point to be and press

E. If you select a point that has been placed on an

object and then move that point, the point will be constrained to the object on which it was placed. For example, a point placed on a circle will remain on that circle regardless of how you move the point.

Midpoint Tap where you want one point to be and press

where you want the other point to be and press point is automatically created midway between those two points.

If you choose an object first—such as a segment—choosing the Midpoint tool and pressing between the ends of that object. (In the case of a circle, the midpoint is created at the circle’s center.)

Center Tap a circle and press

center of the circle.

Intersection Tap the desired intersection and press E. A point is

created at one of the points of intersection.

Keyboard shortcut:

E. A point is created at the

E adds a point midway

E. Tap

E. A

Intersections Tap one object other than a point and press E. Tap

another object and press objects intersect are created and named. Note that an intersections object is created in Symbolic view even if the two objects selected do not intersect.

24 Geometry

E. The point(s) where the two

Random Points Press E to randomly create a point in Plot view.

Continue pressing E to create more random points. Press J when you are done.

Line

Segment Tap where you want one endpoint to be and press E.

Tap where you want the other endpoint to be and press

E. A segment is drawn between the two end points.

Keyboard shortcut: r

Ray Tap where you want the endpoint to be and press E.

Tap a point that you want the ray to pass through and press

E. A ray is drawn from the first point and through the

second point.

Line Tap at a point you want the line to pass through and press

E. Tap at another point you want the line to pass

through and press points.

Keyboard shortcut: Tap a third point (C) and press E. A line is drawn

through A bisecting the angle formed by AB

E. A line is drawn through the two

and AC.

Parallel Tap on a point (P) and press

press

E. A new line is draw parallel to L and passing

through P.

Perpendicular Tap on a point (P) and press E. Tap on a line (L) and

press

E. A new line is draw perpendicular to L and

passing through P.

Tangent Tap on a curve (C) and press E. Tap on a point (P) and

press

E. If the point (P) is on the curve (C), then a single

tangent is drawn. If the point (P) is not on the curve (C), then zero or more tangents may be drawn.

Median Tap on a point (A) and press

E. A line is drawn through the point (A) and the

press midpoint of the segment.

Geometry 25

E. Tap on a line (L) and

E. Tap on a segment and

Altitude Tap on a point (A) and press E. Tap on a segment and

press

E. A line is drawn through the point (A)

perpendicular to the segment (or its extension).

Angle bisector Tap the point that is the vertex of the angle to be bisected (A)

and press

E. Tap another point (B) and press E.

Polygon The Polygon menu provides tools for drawing various

polygons.

Triangle Tap at each vertex, pressing E after each tap.

Keyboard shortcut: n

Isosceles Triangle

Right Triangle Draws a right triangle given two points and a scale factor.

Draws an isosceles triangle defined by two of its vertices and an angle. The vertices define one of the two sides equal in length and the angle defines the angle between the two sides of equal length. Like equilateral_triangle, you have the option of storing the coordinates of the third point into a CAS variable.

isosceles_triangle(point1, point2, angle)

Example:

isosceles_triangle(GA, GB, angle(GC, GA, GB) defines an isosceles triangle such that one of the two sides of equal length is AB, and the angle between the two sides of equal length has a measure equal to that of ∡ ACB.

One leg of the right triangle is defined by the two points, the vertex of the right angle is at the first point, and the scale factor multiplies the length of the first leg to determine the length of the second leg.

right_triangle(point1, point2, realk)

Example:

right_triangle(GA, GB, 1) draws an isosceles right triangles with its right angle at point A, and with both legs equal in length to segment AB.

Quadrilateral Tap at each vertex, pressing

26 Geometry

E after each tap.

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