Question

On a coordinate plane, a line F G goes through (negative 8, negative 8) and (8, 4). Point H is at (6, negative 6).
Which point is on the line that passes through point H and is perpendicular to line FG?

(–6, 10)
(–2, –12)
(0, –2)
(4, 2)

Answer 1

First find the slope of FG: m = (4 − (−8)) / (8 − (−8)) = 12/16 = 3/4.
A perpendicular line has slope −4/3. The line through H(6, −6) is y + 6 = (−4/3)(x − 6).

Test (−6, 10): y + 6 = 10 + 6 = 16 and (−4/3)(x − 6) = (−4/3)(−12) = 16, so it lies on the line.

Answer: (−6, 10).