The line through the points (1,5) and (7,-6) is perpendicular to the line through the points (5,k) and (2,-7). Find the value of k.

Question

Please explain how you did it!

Answer 1

The product of slopes of perpendicular lines equals -1. Find the two slopes, multiply them and set equal to -1, then solve for k.

m₁ = (-6 - 5)/(7 - 1) = -11/6

m₂ = (-7 - k)/(2 - 5) = (7 + k)/3

m₁m₂ = -1

(-11/6) (7 + k) / 3 = -1

You should be able to solve for k and finish from here.