Question

On a coordinate plane, line A B goes through (negative 2, 4) and (0, negative 4). Point Z is at (0, 2).
Which point is on the line that passes through point Z and is perpendicular to line AB?

(–4, 1)
(1, –2 )
(2, 0)
(4, 4)

Answer 1

Slope of AB = (-4 − 4)/(0 − (−2)) = −8/2 = −4.
Perpendicular slope = 1/4. Line through Z(0,2): y = 2 + (1/4)x.
Plug x = −4: y = 2 + (−4)/4 = 1, so (−4, 1) lies on the line.

Answer: (−4, 1)