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How Do You Know if Two Lines Are Perpendicular?

Definition: Perpendicular Lines

Summary

  1. Perpendicular lines intersect each other at a right angle
  2. When you multiply the slopes of two perpendicular lines, you always get -1
  3. The slope of y=2x-2 is 2, and the slope of y=-1/2x+8 is -1/2
  4. 2•-1/2=-1, so the two lines are perpendicular
  5. Horizontal lines have a slope of 0, and vertical lines have undefined slope
  6. Since you can't multiply by 'undefined', the rule doesn't work with horizontal and vertical lines

Notes

    1. Perpendicular lines intersect each other at a right angle
    1. Perpendicular lines intersect each other at a right angle
    1. Perpendicular lines intersect each other at a right angle
    2. So when L1 and L2 cross, they make a right angle
    1. We can see this by looking at the graph
    1. Is there a way we can know for sure without looking at the graph?
    1. If two lines are perpendicular, when you multiply their slopes you always get -1
    1. If you have the equations of two lines, you can use this rule to figure out whether they're perpendicular
    1. y=2x-2 is a line given in slope-intercept form
    2. In slope-intercept form, the slope is just the number in front of the x, which for y=2x-2 is 2
    3. y=-1/2x+8 is a line given in slope-intercept form
    4. The slope of y=-1/2x+8 is -1/2
    1. We can multiply their slopes and see if we get -1
    1. 2•-1/2=-1
    2. This means the lines are perpendicular!
    1. 2•-1/2=-1
    2. This means the lines are perpendicular!
    1. Since we multiplied the slopes and got -1, we know the lines are perpendicular
    1. Horizontal lines run straight across from left to right
    2. Vertical lines run straight up and down
    1. You can tell by looking at the graph that they form a right angle
    1. All horizontal lines have a slope of 0
    1. All vertical lines have an undefined slope
    1. That doesn't make sense!
    2. Multiplying something times 'undefined' doesn't mean anything!
    1. Multiplying something times 'undefined' doesn't mean anything!
    1. This is a special case where the rule doesn't work
    2. You just have to remember that horizontal and vertical lines are always perpendicular to each other
    1. This is a special case where the rule doesn't work
    2. You just have to remember that horizontal and vertical lines are always perpendicular to each other
    1. But in any other case, the rule will work
    2. All you have to do is multiply the slopes to see if you get -1
    3. If you do, the two lines are perpendicular!