Question

which point on the y-axis lies on the line that passes through point c and is perpendicular to line ab?
options:
(-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: Equation of line through C(6, 4)

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

Step4: Find y - intercept (x = 0)

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

Answer:

(0, 2)