Frequently Asked Questions
How do you find the slope of a perpendicular line?
Take the negative reciprocal. If the reference slope is m and is not zero, the perpendicular slope is minus one divided by m. For zero slope, the perpendicular is vertical.
Why is the slope product minus one?
For two non-vertical lines to meet at a right angle, their slopes m and m prime satisfy m times m prime equals minus one - a consequence of the dot product of their direction vectors equaling zero.
What if the original line is vertical?
A vertical line has the form x equals constant. Any horizontal line y equals constant is perpendicular to it.
What is the slope of a line perpendicular to y = mx + b?
It is the negative reciprocal, −1/m. For example a line with slope 2 has perpendiculars with slope −1/2. A horizontal line (slope 0) is perpendicular to a vertical line (undefined slope).
Are perpendicular slopes always negative reciprocals?
Yes, two non-vertical lines are perpendicular exactly when the product of their slopes is −1, which makes each slope the negative reciprocal of the other. The only exception is the horizontal-vertical pair, where one slope is undefined.
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