Explorations in Geometry
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.
- Open a new sketch and select "create axes" and "snap to grid" from the Graph menu.
- Create a point (Point C-move me) somewhere on the graph but NOT on either of the two axes.
- 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)
- Construct a line Parallel to the x-axis passing through C, and construct a point at the intersection with the y-axis (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.
- 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.
- Use the Measure menu to find the equation of the line.
- Move point C right and left and look at the measurements you have made. Can you explain what happens.
- Move point C up and Down and look at the measurements. Can you predict what the equation will say?
- 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?
- If you ONLY knew the equation of the line, could you find the coordinates of the x- and y-intercepts?
- What other observations can you make about the line? Write a brief paragraph to describe your conjectures.