Question

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)

Explanation:

Step1: Find slope of MN

Points \( M(-4, 0) \), \( N(4, 2) \). Slope \( m_{MN} = \frac{2 - 0}{4 - (-4)} = \frac{2}{8} = \frac{1}{4} \).

Step2: Find slope of perpendicular line

Perpendicular slope \( m = -4 \) (negative reciprocal of \( \frac{1}{4} \)).

Step3: Find equation of line through P(2, -4)

Using point - slope form \( y - y_1 = m(x - x_1) \): \( y - (-4) = -4(x - 2) \) → \( y + 4 = -4x + 8 \) → \( y = -4x + 4 \).

Step4: Find x - intercept (y = 0)

Set \( y = 0 \): \( 0 = -4x + 4 \) → \( 4x = 4 \) → \( x = 1 \). So the point is \( (1, 0) \).

Answer:

C. (1, 0)