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

Slope of line through (– 2, 6) and (4, 8). 

m₁ = \(\frac{8-6}{4-(-2)}=\frac{1}{3}\) 

and, slope of line through (8, 12) and (x, 24), 

m₂= \(\frac{24-12}{x-8}=\frac{12}{x-8}\)

Since the lines are perpendicular, So, m₁m₂ = – 1 ⇒ \(\frac{1}{3}.\frac{12}{x-8}=-1\) 

⇒ 4 = – x + 8 

⇒ x = 4