[color=#000000]The following applet demonstrates a property that parallel lines have when they're drawn in the coordinate plane. [br] [i] [br]Be sure to move the [color=#1e84cc][b]blue points[/b][/color] around quite a bit![/i] [/color]
QUESTION 1
If you move the blue points to make the lines vertical, are the lines considered parallel?
No, since the two lines overlap they are coinciding. However, vertical line are still considered parallel when they are not coinciding.
[color=#000000]What can you conclude about parallel lines drawn in the coordinate plane? [/color]
[color=#000000]They have the [/color][color=#741b47]same gradient[/color][color=#000000] yet different [/color][color=#741b47]y-intercepts[/color][color=#000000]. [/color]
PERPENDICULAR LINES
[color=#000000]This applet demonstrates a property that perpendicular lines have when they're drawn in the coordinate plane. [br][br][i]Be sure to move the points around quite a bit and observe carefully as you do! [/i][/color]
[color=#000000]Multiple the gradient of each line. What do you notice?[/color]
They always equal -1
[color=#000000]What can you conclude about the gradients of perpendicular lines that are drawn in the coordinate plane? [br][/color]
[color=#000000]If two perpendicular lines are drawn in the coordinate plane, then their slopes are always opposite reciprocals. Another way of expressing this fact is that their slopes always multiply to -1. [/color]