Question

which point on the y-axis lies on the line that passes through point c and is perpendicular to line ab?
○ (-6, 0)
○ (0, -6)
○ (0, 2)
○ (2, 0)

Explanation:

Step1: Find slope of AB

Points A(-2, 4) and B(2, -8). Slope \( m_{AB} = \frac{-8 - 4}{2 - (-2)} = \frac{-12}{4} = -3 \).

Step2: Find slope of perpendicular line

Perpendicular slope \( m = \frac{1}{3} \) (negative reciprocal of -3).

Step3: Use point C(6, 4) to find equation

Using point - slope form \( y - y_1 = m(x - x_1) \): \( y - 4 = \frac{1}{3}(x - 6) \). Simplify: \( y - 4 = \frac{1}{3}x - 2 \), so \( y = \frac{1}{3}x + 2 \).

Step4: Find y - intercept (x = 0)

Substitute x = 0: \( y = \frac{1}{3}(0) + 2 = 2 \). So the point is (0, 2).

Answer:

(0, 2)