Explorations in Geometry

with the

Geometerís 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.

    1. Open a new sketch and select "create axes" and "snap to grid" from the Graph menu.
    2. Create a point (Point C) somewhere on the graph but NOT on either of the two axes.
    3. 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)
    4. Construct a line Perpendicular to the x-axis passing through C, and construct a point on this line (Point E)
    5. Now hide both the lines you have created, and create a line containing points D and E, and make it a unique color.
    6. Create line segments CD and CE ?
    7. Use the Measure menu to find the equation of the line, the length of the two segments CD and CE, and the coordinates of Point D
    8. 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.
    9. Move point C up and Down and look at the measurements. Can you determine a relationship?
    10. What if you move point C ABOVE point E? What if you move point C to the LEFT of point D?
    11. If you ONLY knew the coordinates of D and E, could you find the equation of the line? How would you do it?
    12. What other observations can you make about the line? Write a brief paragraph to describe your conjectures.