Question

The value of x for which the line through A(-2, 6) and B(4, 8) is perpendicular to the the line through the points
C(8, 12) and D(x, 24) is .

• A. 4
• B. 1
• C. 6
• D. 8

Answer 1

The correct option is A 4

Let the slope of AB be $m_1$ and the slope of CD be $m_2$.
As AB is perpendicular to CD,
$\Rightarrow m_1\times m_2=-1\Rightarrow \frac{8-6}{4-\left(-2\right)}\times \frac{24-12}{x-8}=-1\Rightarrow \frac{2}{6}\times \frac{12}{x-8}=-1\Rightarrow \frac{4}{x-8}=-1\Rightarrow 8-x=4\Rightarrow x=4$