Question

line throgh the points $(-2,6)$ and $(4,8)$ is perpendicular to the line through the points $(8,12)$ and $(x,24)$ find the value of x

Answer 1

let $A(-2,6)B(4,8)C(8,12)D(x,24)$

let slope of line $AB=m_1$

let slope of line $CD=m_2$

As given in question we have $m_1.m_2=-1$

Here $m_1=\frac{8-6}{4-(-2)}=\frac{2}{6}=\frac{1}{3}$

$m_2=\frac{24-12}{x-8}=\frac{12}{x-8}$

$m_1\times m_2=-1\Rightarrow \frac{1}{3}\times \frac{12}{x-8}=-1$

$\frac{4}{x-8}=-1\Rightarrow 4=-(x-8)$

$4=-x+8$

$x=8-4$

$x=4$.