Explorations in Geometry

with the

Geometerís Sketchpad

Exploration 12

This exploration will extend your understanding 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-move me) somewhere on the graph but NOT on either of the two axes.
    3. Now construct a line Perpendicular to the x-axis passing through point C. Create a new point at the intersection of this line and the x-axis (Point D)
    4. Construct a line Parallel to the x-axis passing through C, and construct a point at the intersection with the y-axis (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. The points E and D are called the y-intercept and the x-intercept of the line. Measure the coordinates of points D and E.
    7. Use the Measure menu to find the equation of the line.
    8. Move point C right and left and look at the measurements you have made. Can you explain what happens.
    9. Move point C up and Down and look at the measurements. Can you predict what the equation will say?
    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. If you ONLY knew the equation of the line, could you find the coordinates of the x- and y-intercepts?
    13. What other observations can you make about the line? Write a brief paragraph to describe your conjectures.