Line through the points (-2, 6) and (4, S) is perpendicular to the lin

1.	Line through the points (-2, 6) and (4, S) is perpendicular to the line through the points (8,12) and (x, 24). Find the value of x
Answer» Slope of the line passing through the points (-2, 6) and (4, 8) is m₁ = (8 - 6)/(4 - (-2)) = 2/6 = 1/3 Slope of the line passing through the points (8, 12) and (x, 24) is m₂ = (24 - 21)/(x - 8) = 12/(x - 8) Since the lines are perpendicular then m₁ x m₂ = - 1 i.e, 1/3 x 12/(x - 8) = -1 i.e., 4 = - x + 8 ⇒ x = 4

Line through the points (-2, 6) and (4, S) is perpendicular to the line through the points (8,12) and (x, 24). Find the value of x

Answer»

Slope of the line passing through the points (-2, 6) and (4, 8) is

m₁ = (8 - 6)/(4 - (-2)) = 2/6 = 1/3

Slope of the line passing through the points (8, 12) and (x, 24) is

m₂ = (24 - 21)/(x - 8) = 12/(x - 8)

Since the lines are perpendicular then m₁ x m₂ = - 1

i.e, 1/3 x 12/(x - 8) = -1

i.e., 4 = - x + 8 ⇒ x = 4