Respuesta :

Let's use an example

Say we had two lines P and Q. If P has slope 2/5, then Q must have slope -5/2 in order for P and Q to be perpendicular.

Note how -5/2 is the negative reciprocal of 2/5. In other words, you flip the fraction and the sign to go from either slope.

Another thing to notice is that the two slopes multiply to -1. This is true for any pair of perpendicular lines as long as neither line is vertical.

sqdancefan

Answer:

  The product of the slopes of perpendicular lines is -1.

Step-by-step explanation:

With one exception, the product of the slopes of perpendicular lines is -1. So, if the slopes are 'a' and 'b', we have ...

  a·b = -1

  a = -1/b  . . .  solve for a in terms of b

  b = -1/a  . . .  solve for b in terms of a

This tells you that each slope is the negative reciprocal of the other.

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The exception is horizontal and vertical lines. The slope of a horizontal line is 0; the slope of a vertical line is "undefined." While -1/0 is "undefined", the reverse is not necessarily true: -1/"undefined" is not necessarily zero.

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