B. Slope and Perpendicular Lines
B. Slope and Perpendicular Lines
You've seen that there is a relationship between the slopes of parallel lines. Do you think there is also a relationship between the slopes of perpendicular lines? The following Investigation explores this question.
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Perpendicular Lines
lines that are perpendicular meet at right angles |
Investigation
The applet shows a line segment,
AB. This segment can be adjusted by moving points
A and
B. Changing the rotation angle will produce another line segment
AC, where angle
CAB is equal to the rotation angle.
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What rotation angle produces perpendicular line segments?
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With the rotation angle set to 90º, determine the slopes of line segments AB and AC. Enter these values into the table below, as fractions. Move A and B, and repeat the procedure for several pairs of line segments. Keep the rotation angle set to 90º.
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Suggest a relationship between the slopes of perpendicular lines.
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If a line has a slope of
, what is the slope of a line perpendicular to it?
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If a line has a slope of -3.25, what is the slope of a line perpendicular to it?
Alternate Investigation
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If you are not able to access the Perpendicular Lines applet, complete Investigating Slopes of Parallel and Perpendicular Lines on pp. 383 - 384 of Mathematics 10. |