Watching 'Em Dance
Wanna watch some dancing pairs?
OBJECTIVE: To understand the properties of parallel and perpendicular lines
[br]Up to this point, you've studied the properties of lines, but only as [color=#0000ff]single[/color] lines.[br][br]In this lesson, you'll learn about the properties of [color=#0000ff]pairs[/color] of lines. In particular, you'll look at the behavior of [color=#0000ff]parallel lines[/color] and [color=#0000ff]perpendicular lines[/color] as they dance across the Cartesian plane.
[color=#000000]The following applet demonstrates a property that [/color][color=#0000ff]parallel lines[/color][color=#000000] have when they're drawn in the Cartesian plane. Watch how the pair moves as you drag the [/color][color=#3d85c6][b]haloed [/b][/color][color=#1e84cc][b]blue point[/b][/color] from quadrant to quadrant.[color=#000000][br] Be sure to move the [color=#1e84cc][b]blue points[/b][/color] around quite a bit! [/color]
[color=#0000ff][b]QUESTION[/b][/color][color=#000000][b]:[/b] What can you conclude about parallel lines drawn in the coordinate plane? Pay particular attention to the [/color][b][color=#3d85c6]blue dots[/color][/b][color=#000000] and the [/color][b][color=#ff0000]red triangles[/color].[/b]
NOW let's watch the second pair!
[color=#000000][br]This applet demonstrates a property that [/color][color=#0000ff]perpendicular lines[/color][color=#000000] have when they're drawn in the Cartesian plane. [br][br]Be sure to move the points around quite a bit and observe carefully as you do! [/color]
[b][color=#0000ff]QUESTION:[/color][/b] What can you conclude about perpendicular lines that are drawn in the coordinate plane? [br](Assume the lines are not aligned horizontally and vertically).
NOW let's do some pencil pushing!
[br]The applet below will drill you on finding the equation of a line[color=#0000ff] parallel[/color] or [color=#0000ff]perpendicular[/color] to a given line and passing through a given point.[br][br]You already have a point. You can get the slope from the given line. So you can use the [color=#0000ff]POINT-SLOPE FORM[/color] of the line to get started. Just make sure you use the correct slope in getting the equation of the line you want. Keep the relationships you discovered earlier in mind.[br]
That's all for now, folks!
[br]Next time, we'll look at more pairs of lines.[br][br]So what's your biggest takeaway for this lesson?