The geometric objects discussed in this section are those that can be created 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 151.
In Plot view, you choose 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 J. (You can tell if a drawing tool is still active by the presence of on-screen help in the top left-side corner of the screen, help such as Hit Point 1.)
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. However, you can also use the cursor keys to position the cursor where you want the point to be and then press E.
The drawing tools for the geometric objects listed in this section can be selected from the menu buttons a the bottom of the screen. Some objects can also be entered using a keyboard shortcut. For example, you can select the triangle drawing tool by pressing n. (Keyboard shortcuts are only available if they ave been turned on in Plot Setup view. See page 134.)
Points
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 E. 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.
If there is no object where you tap, a point is created if you then press E.
Midpoint Tap where you want one point to be and press E. Tap where you want the other point to be and press E. A 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 E adds a point midway between the ends of that object. (In he case of a circle, the midpoint is created at the circle’s center.)
Intersection Tap one of the two intersecting objects and press E. Tap the other object and press E. A point is created at one of the points of intersection.
Keyboard shortcut: g More
Trace Displays a list of points for you to choose the one you want to trace. If you subsequently move that point, a trace line is drawn on the screen to show its path. In the example at the right, point B was chosen to
be traced. When that point was moved—up and to the left—a path of its movement was created.
Trace creates an entry in Symbolic view. In the example above, the entry is Trace(GB).
Stop Trace Turns off tracing and deletes the definition of the trace point from Symbolic view. If more than one point is being traced, a
menu of trace points appears so that you can choose which one to untrace.
Untrace does not erase any existing trace lines. It merely prevents any further tracing should the point be moved again.
Erase Trace Erases all trace lines, but leaves the definition of the trace points in Symbolic view. While a Trace definition is still in Symbolic view, if you move the point again, a new trace line is created.
Center Tap a circle and press E. Element 0 .. 1 ???????????
Intersections Tap one object and press E. Tap another object and press E. Each point of intersection is labeled (and labeled) identically. Note that an intersections object is created in Symbolic view even if the two objects selected do not intersect.
Random pts Displays a palette for you to choose to add 1, 2, 3, or 4 points. The points are placed randomly.
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 E. A line is drawn the two points.
Keyboard shortcut: j
Vector Tap where you want one endpoint to be and press E. Tap where you want the other endpoint to be and press E. A vector is drawn between the two end points.
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. Tap a third point (C) and press E. A line is drawn through A bisecting the angle formed by AB and AC.
Perpend-icular
bisector Tap one point on the line (L) you want to bisect and press E. Tap another point on L and press E. A line is drawn perpendicular to L and equidistant from the two points you tapped.
You can also draw a perpendicular bisector to a line that doesn’t exist. Just tap and press E at one point and do the same at another point. A line is drawn perpendicular to the imaginary line between the two points and equidistant from both points.
If you are drawing a perpendicular bisector to a segment, choose the segment first and then select Perp. Bisector from the Line menu. The bisector is drawn immediately without you having to select any points. Just press E to save the bisector.
Parallel Tap on a point (P) and press E. Tap on a line (L) and press E. A new line is draw parallel to L and passing through P.
Perpend-icular 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. A one or more lines are drawn from P tangent to C.
Median Tap on a vertex (A) and press E. tap on the line opposite the vertex and press E. A line is drawn through A that crosses segment BC equidistant from both endpoints.
Altitude Tap on a vertex (A) and press E. tap on the line opposite the vertex and press E. A line is drawn through A that crosses segment BC at right angles.
Polygon
The Polygon menu provides tools for drawing various polygons.Triangle Tap at each vertex, pressing E after each tap.
Keyboard shortcut: n
Quadilateral Tap at each vertex, pressing E after each tap.
Ngon
Polygon5 Produces a pentagon. Tap at each vertex, pressing E after each tap.
Polygon6 Produces a hexagon. Tap at each vertex, pressing E after each tap.
Hexagon Produces a regular hexagon (that is, one with sides of equal length). Tap at each vertex, pressing E after each tap.
Special
Eq. triangle Produces an equilateral triangle. Tap at one vertex and press E. Tap at another vertex and press E. The location of the third vertex is automatically calculated and the triangle is drawn.
Square Tap at one vertex and press E. Tap at another vertex and press E. Tap at a third vertex and press E. The location of the fourth vertex is automatically calculated and the square is drawn.
Parallel-ogram Tap at one vertex and press E. Tap at another vertex and press E. Tap at a third vertex and press E. The location of the fourth vertex is automatically calculated and the parallelogram is drawn.
Curve
Circle Tap at the center of the circle and press E. Tap at point on the circumference and press E. A circle is drawn about the center point with a radius equal to the distance between the two tapped points.
Keyboard shortcut: F
You can also create a circle by first defining in Symbolic view.
The syntax is circle(GA,GB) where A and B are two points. A circle is drawn in Plot view such that A and B are on the circumference.
Ellipse Tap at one focus point and press E. Tap at the second focus point and press E. Tap at point on the
circumference and press E.
Hyperbola Tap at one focus point and press E. Tap at the second focus point and press E. Tap at point on one branch of the hyperbola and press E.
Parabola Tap at the focus point and press E. Tap either on a line (the directrix) or a point (the vertex) and press E. Special
Circumcircle A circumcircle is the circle that passes through each of the triangle’s three vertices, thus enclosing the triangle.
Tap at each vertex of the triangle, pressing E after each tap.
Incircle An incircle is a circle that is tangent to each of a polygon’s sides. The HP Prime can draw an incircle that is tangent to the sides of a triangle.
Tap at each vertex of the triangle, pressing E after each tap.
Excircle If you extend two sides of a triangle in the direction opposite their common vertex and then draw a circle tangent both to these lines and to the third side of the triangle, you have an excircle.
Tap at each vertex of the triangle, pressing E after each tap.
The excircle is drawn tangent to the side defined by the last two vertices tapped. In the example at the right, the last two vertices tapped were A
and C (or C and A). Thus the excircle is drawn tangent to the segment AC.
Locus ???????????
Plot You can plot expressions of the following types in Plot view:
• Function
• Parametric
• Polar
• Sequence
• Slopefield
Tap , select Plot, and then the type of expression you want to plot. The entry line is enabled for you to define the expression.
Note that the variables you specify for an expression must be in lowercase.
In this example, Function has been selected as the plot type and the graph of y = 1/
x is plotted.