Question

Find the slope of the line perpendicular to $AB$ where $A(5,-6)$ and $B(2,-7)$.

• A. $-2$
• B. $-3$
• C. $1$
• D. $2$

Answer 1

Answer: (B)

$-3$

The slope $m$ of the line passing through the points $(x_1,y_1)$ and $(x_2,y_2)$ is

$m=\frac{y_2-y_1}{x_2-x_1}$

Therefore, the slope of the line passing through the points $(5.-6)$ and $(2,-7)$ is:

$m=\frac{-7-(-6)}{2-5}=\frac{-7+6}{-3}=\frac{-1}{-3}=\frac{1}{3}$

Since the slope of the line perpendicular to the line is the negative reciprocal,

Hence, the slope of the line is $-3$.