Intersecting Lines

CLICKING HERE WILL OPEN A WINDOW WITH THE INTERSECTING LINE APPLET

Dragging the mouse with a button down on a colored square will move the same colored line without changing its slope. Doing this on a colored circle will rotate the line centered on the position of the square. Such changes will also change the equation of the corresponding line which is given in slope-intercept form in the lower left corner. Also in the lower left corner, the point of intersection and the angle between the lines is provided. In the lower right corner, the coordinates of the colored squares and circles are provided.

Suppose l is the line through the points (2,4) and (5,-2). It will be helpful to start with the red square at (2,4) and the red circle at (5,-2).

1. Drag the mouse on the red square and move the line around to different spots. What happens to the equation of the red line as you do this? If you now move the yellow line to go through points (2,4) and (5,-2), what can you say about the yellow and red lines?
2. Now, move the red square to coordinates (0,3) and leave it there. Use the red circle to move the red line around. What happens to the its equation now? What happens if you repeat this experiment after moving the red square to some other point on the y-axis?
3. With the yellow line still through points (2,4) and (5,-2), can you find an equation for the line passing through (0,1) and parallel to the yellow line?
4. How might you find an equation for the line passing through (1,1) and parallel to the yellow line?
5. Now, try to find a red line that is perpendicular to the yellow line. To do this, what should the angle between the lines be (in radians?) Once you have done this, examine the slopes of the two lines.
6. Find some other pairs of perpendicular lines with other slopes. Compare the slopes of the lines as you find such pairs. You should see a pattern emerging.

If you're having difficulties, here's a brief lesson on lines.