Respuesta :
The slope of line "v" is [tex]\frac{8}{5}[/tex]
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
[tex]\text {slope of line } w \times \text { slope of line } v=-1[/tex] ---- eqn 1
Let us first find slope of line w
The slope "m" of a line is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\text {Here } x_{1}=-4 \text { and } x_{2}=12 \text { and } y_{1}=8 \text { and } y_{2}=-2[/tex]
[tex]m=\frac{-2-8}{12-(-4)}=\frac{-10}{16}=\frac{-5}{8}[/tex]
Thus the slope of line "w" is [tex]\frac{-5}{8}[/tex]
Substituting the slope of w in eqn 1 we get,
[tex]\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}[/tex]
Thus the slope of line "v" is [tex]\frac{8}{5}[/tex]
