Question

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

$\text{Let the given pionts be A (-2, 6), B(4, 8), P (8, 12) and Q (x, 24).}\text{Slope of}AB=m_1=\frac{8-6}{4+2}=\frac{2}{6}=\frac{1}{3}\text{Slope of}PQ=m_2=\frac{24-12}{x-8}=\frac{12}{x-8}\text{It is given that the line joining A (-2, 6) and B (4, 8) and the line joining P (8, 12) and Q (x, 24) are perpendicular.}\therefore m_1{m}_2=-1\Rightarrow \frac{1}{3}\times \frac{12}{x-8}=-1\Rightarrow x-8=-4\Rightarrow x=4\text{Hence, the value of x is 4.}$