Question

If the line through 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) and D(x, 24) be the given points.

Let $m_1$ and $m_2$ be the slopes of AB and CD respectively. Then,

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

$m_2$ = slope of CD = $\frac{(24-12)}{(x-8)}=\frac{12}{(x-8)}$

Now, $AB\perp CD\iff m_1{m}_2=-1$

$\iff \frac{1}{3}\times \frac{12}{(x-8)}=-1$

$\iff -x+8=4\iff x=4$

Hence, the required value of x is 4.