Question

On a coordinate plane, line M N goes through (negative 4, 0) and (4, 2). Point P is at (2, negative 4).
Which point on the x-axis lies on the line that passes through point P and is perpendicular to line MN?

(0, 1)
(0, 4)
(1, 0)
(4, 0)

Answer 1

Slope of MN = (2 - 0)/(4 - (−4)) = 2/8 = 1/4, so the perpendicular slope = −4.

Line through P(2, −4) with slope −4: y + 4 = −4(x − 2) → y = −4x + 4.

Set y = 0 for the x-axis: 0 = −4x + 4 → x = 1.

So the point is (1, 0).