Question

Slope of the straight line which is perpendicular to the straight line joining the points $(-2,6)$ and $(4,8)$ is equal to:

• A. $\frac{1}{3}$
• B. $3$
• C. $-3$
• D. $-\frac{1}{3}$

Answer 1

The correct option is C $-3$

Product of slopes of perpendicular lines is equal to $-1$.

Let us find the slope of line passing through points $(-2,6)$ and $(4,8)$,call that slope as $m1$

So slope of line passing through points $(x1,y1)$ and $(x2,y2)$ is given as $\frac{y2-y1}{x2-x1}$

So $m1=\frac{8-6}{4-(-2)}$

$⟹m1=\frac{1}{3}$

lets us call the slope of perpendicular line as $m2$

So product of slopes of perpendicular lines is $m1\times m2=-1$

$\frac{1}{3}\times m2=-1$

$m2=-3$

So the straight line which is perpendicular to the straight line joining the points (-2,6) and (4,8) is equal to $-3$