Explorations in Geometry

with the

Geometer’s Sketchpad

Exploration 11

This exploration should help you understand more about the equations of a line on the coordinate plane. When your done, your sketch should look something like the picture.

- Open a new sketch and select "create axes" and "snap to grid" from the
__G__raph menu. - Create a point (Point C) somewhere on the graph but NOT on either of the two axes.
- Now construct a line parallel to the x-axis passing through point C. Create a new point at the intersection of this line and the y-axis (Point D)
- Construct a line Perpendicular to the x-axis passing through C, and construct a point on this line (Point E)
- Now hide both the lines you have created, and create a line containing points D and E, and make it a unique color.
- Create line segments CD and CE ?
- Use the
__M__easure menu to find the equation of the line, the length of the two segments CD and CE, and the coordinates of Point D - Move point C right and left and look at the measurements you have made. Can you determine a relationship? You might want to add one more measurement, the ratio of CE to CD.
- Move point C up and Down and look at the measurements. Can you determine a relationship?
- What if you move point C ABOVE point E? What if you move point C to the LEFT of point D?
- If you
**ONLY**knew the coordinates of D and E, could you find the equation of the line? How would you do it? - What other observations can you make about the line? Write a brief paragraph to describe your conjectures.