Question

which point on the x-axis lies on the line that passes through point c and is parallel to line ab? (1, 0) (1, 1) (0, 2) (2, 0)

Explanation:

Step1: Find slope of AB

Points A(-4, 0) and B(2, -3). Slope \( m = \frac{-3 - 0}{2 - (-4)} = \frac{-3}{6} = -\frac{1}{2} \).

Step2: Equation of line through C

Point C(-2, 2), slope \( -\frac{1}{2} \). Using point - slope: \( y - 2 = -\frac{1}{2}(x + 2) \).
Simplify: \( y - 2 = -\frac{1}{2}x - 1 \), so \( y = -\frac{1}{2}x + 1 \).

Step3: Find x - intercept (y = 0)

Set \( 0 = -\frac{1}{2}x + 1 \). Solve: \( \frac{1}{2}x = 1 \), \( x = 2 \). So the point is (2, 0).

Answer:

(2, 0)