Question

If the line passes 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 the points be A(-2, 6), B(4, 8), C(8, 12) and D(x, 24).

Let $m_1$ and $m_2$ be the sloped 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, according to the question, $AB\perp CD$

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

$\Rightarrow x-8=-4\Rightarrow x=4$

Hence, the required value of x is 4.