Question

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)

On a coordinate plane, line P Q goes through (negative 6, 4) and (4, negative 4). Point R is at (4, 2).

Answer 1

Slope of PQ = (-4 - 4)/(4 - (-6)) = -8/10 = -4/5, so the perpendicular slope is 5/4.

Equation of the line through R(4,2): y - 2 = (5/4)(x - 4).

Test (−4, −8): y - 2 = (−8) - 2 = −10; right side = (5/4)(−4 - 4) = (5/4)(−8) = −10. Matches.

So (−4, −8) is on the perpendicular line.