Question

On a coordinate plane, line P Q goes through (negative 6, 4) and (4, negative 4). Point R is at (4, 2).
Which point is on the line that passes through point R and is perpendicular to line PQ?

(–6, 10)
(–4, –8)
(0, –1)
(2, 4)

Answer 1

Slope of PQ = (-4 - 4)/(4 - (-6)) = -8/10 = -4/5.
Perpendicular slope = 5/4. Line through R(4,2): y - 2 = (5/4)(x - 4).

Check (–4, –8): slope from R to that point = (-8 - 2)/(-4 - 4) = -10/-8 = 5/4, so it lies on the perpendicular.

Answer: (–4, –8).