Question

Line w and line v are perpendicular to each other. Line w passes through the points ( -4,8 ) and ( 12,-2 ). What is the slope of line v?

Answer 1

The slope of line "v" is $\frac{8}{5}$

Solution:

Given that Line w and line v are perpendicular to each other

Also given that line w passes through the points ( -4, 8 ) and ( 12, -2 )

To find: slope of line v

Since line w and line v are perpendicular to each other, product of slopes of line w and line v are equal to -1

$\text {slope of line } w \times \text { slope of line } v=-1$  ---- eqn 1

Let us first find slope of line w

The slope "m" of a line is given as:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text {Here } x_{1}=-4 \text { and } x_{2}=12 \text { and } y_{1}=8 \text { and } y_{2}=-2$

$m=\frac{-2-8}{12-(-4)}=\frac{-10}{16}=\frac{-5}{8}$

Thus the slope of line "w" is $\frac{-5}{8}$

Substituting the slope of w in eqn 1 we get,

$\begin{array}{l}{\frac{-5}{8} \times \text { slope of line } v=-1} \\\\ {\text { slope of line } v=\frac{8}{-5} \times-1=\frac{8}{5}}\end{array}$

Thus the slope of line "v" is $\frac{8}{5}$