TI-Nspire gives you the option of adding geometric objects (points, perpendicular lines, circles, polygons, and so on) to your Graphs page. These objects can add some type of functionality to your graph or serve as a way of enhancing the overall look of the Graphs page.

Here is how the Perpendicular tool can be used to investigate slope:

Open a new Graphs page by pressing [DOC]→Insert→Graphs.

Press [MENU]→View→Show Grid.

Construct a line by pressing [MENU]→Points & Lines→Line. Click on two grid points to draw the line.

Make sure that you are pointing to a grid point when you draw your line to ensure that the line has a slope with integer values for the rise and run. The first screen shows the line.

Represent the rise and run of slope using the Perpendicular tool to draw two lines. Press [MENU]→Construction→Perpendicular.

Use the

*x*- and*y*-axes to draw perpendiculars to each of the points on the line that represent the rise and run of the line. To draw a perpendicular, click the axis and then the point through which you want the perpendicular line to cross.The second screen shows the result of constructing the two perpendicular lines.

Use the Point tool to place a point on the intersection of the perpendicular lines. Press [MENU]→Points & Lines→Point. Click the point of intersection.

Draw segments that overlay the perpendicular lines to represent the rise and run. Press [MENU]→Points & Lines→Segment.

Press [ESC] to exit the Segment tool.

Hide the perpendicular lines. Right-click ([CLICK][MENU]) each of the perpendicular lines, choose Hide, and click each of the lines.

Now, you have a right triangle with the hypotenuse extended on a graph page. Right-click the two segments to change the attributes of the line style to Dashed. Then, change the attributes of the endpoints that intersect the original line to be Empty Large to make the points look hollow.

Many TI-Nspire authors use a hollow point to signal to the user that the point is movable. The third screen shows the finished product.

Be sure to check and make sure that your rise and run work properly. If you grab and move one of the hollow points **(****[CTRL][CLICK]**), the segments representing rise and run will continue to form a right triangle.

You cannot change the coordinates of the points of intersection with the graphed functions. These points are constrained by the perpendicular line, which is dependent on the hollow point constructed on the *x*-axis. If you try to make a change, you get the message “Cannot accept change: Invalid input.”