Line through the points (– 2, 6) and (4, 8) is perpendicular to the

1.	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» 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

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»

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