## The Geometer's Sketchpad Introductory Lab - page 7

### Mike Riedy

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## Part V: Graphing

One of the new functions added to GSP is the ability to graph points and lines on coordinate axes. Start with a new sketch. Under the GRAPH menu choose "Create Axes". An x-axis and a y-axis should appear. Notice there are already two points on the axes: one at the origin (0, 0) and one at (1, 0). The point at (1, 0) is called the control point. It changes the scale of the axes. Try dragging the control point.

What is the distance between the control point and the origin?

_______________________

Move the control point until the distance is as close to 1 cm as possible. Go back under the GRAPH menu and choose "Show Grid". A bunch of dots appear. Now choose "Snap To Grid" under the GRAPH menu so that there is no check in front of it. Now you should be ready to rock-n-roll.

Let's plot some points. There are two ways to do this. Just like when constructing segments you can do it yourself or have the computer do it for you.

You do it first. Use the point tool to put three points anywhere on the screen. Want to know what the coordinates of the three points are? Highlight each point and go under the MEASUREMENT menu and choose "Coordinate".

What are the coordinates of the three points?

______________ , ______________ , ______________

Now let the computer plot some points. Start with a new sketch and create a axes like you did above. Under the GRAPH menu choose "Plot points...". You should see a screen like the one below.

Have the computer plot the following points: (0, 5), (4, 2), (­4, 2), (­3, ­ 4), and (3, ­4). Now connect each point with a segment to all of the other points.

How many segments did you need to draw? _________________________

The segments that connect points not next to each other are called diagonals.

How many of the segments are diagonals? _________________________

You should now have a pretty picture. Save the sketch to your disk as "Point plot" and draw what you see on the picture below. Now we are going to graph a line. Start with a new sketch. Create axes as previously discussed. Plot the points (4.1, ­3.4) and (­1.7, 5.2). Now have the computer construct the line through the two points. (Remember to switch from the segment tool to the line tool in the toolbox at the left.) Under the MEASUREMENT menu choose "Equation".

What is the equation of the line? _________________________

Measure the slope of the line. What is the slope? _________________________

Highlight the line and one of the points on the line. Choose "Perpendicular line" from under the CONSTRUCT menu.

What is the slope of the perpendicular line? _________________________

Use the computer to multiply the two slopes together. (see p. 8 to refresh on calculator use)

What is the answer? _________________________

#### Summary

We have covered a lot of material in a short period of time. Not only did this lab introduce you to Geometer's Sketchpad but it should also act as a reference guide when we do future activities. Don't lose it. Keep the lab and bring it with you when we come back to the computer lab. You need to turn in both your disk and your lab for grading. Have a great day!!