Bunuel wrote:
If line l is perpendicular to line k, which of the following must be true?
A. The slopes of l and k are equal.
B. The product of the slopes of l and k is 1.
C. The product of the slopes of l and k is −1.
D. The y-intercepts l and k are equal.
E. The x-intercepts of l and k are equal.
Since line l is perpendicular to line k, their slopes are negative reciprocals of each other, and thus the product of their slopes is -1.
For example, if the slope of line k = 2/3, then the slope of line l, which is perpendicular to line k, is -3/2. The product of their slopes is (2/3) x (-3/2) = -1. This is a property of any two lines that are perpendicular to each other, as long as the slope of neither line is 0.
Answer: C
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