How do you know if two line segments are perpendicular

Asked by admin @ in Mathematics viewed by 278 People

How do you know if two line segments are perpendicular?

A. The slope of one is the negative of the slope of the other.
B. Their slopes are reciprocals.
C. Their slopes are negative reciprocals.
D. Their slopes are equal.

Answered by admin @


Answer:  The correct option is

(C) Their slopes are negative reciprocals.

Step-by-step explanation:  We are given to select the correct reason for two line segments to be perpendicular.

We know that

If two line segments are perpendicular, then the product of their slopes is - 1.

Let, m and n represents the slopes of two lines that are perpendicular to each other.

Then, we must have

m\times n=-1\\\\\\\Rightarrow m=-\dfrac{1}{n}~~~~~\textup{and}~~~~~n=-\dfrac{1}{m}.

This implies that m is the negative reciprocal of n and n is the negative reciprocal of m.

Thus, the slopes are negative reciprocals.

Option (C) is CORRECT.


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