Question

Find the slope of the line perpendicular to AB if:

$\left(i\right)A=(0,-5)\text{and}B=(-2,4)$

Answer 1

Finding the slope of the line perpendicular to AB

Given, points are $A(0,-5)\text{and}B(-2,4).$

$\because \text{slope of line AB}=\frac{y_2-y_1}{x_2-x_1}$

$\Rightarrow$ slope $=\frac{4-(-5)}{-2-0}=\frac{4+5}{-2}=-\frac{9}{2}$

We know, if two lines are perpendicular, the

product of their slopes is $-1$.

$\therefore \text{slope of line perpendicular to AB}$

= $\frac{-1}{\text{slope of AB}}=\frac{-1}{-\frac{9}{2}}=\frac{2}{9}$

Hence, the slope of the line perpendicular to AB is $\frac{2}{9}$.