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: $y - 2 = -\frac{1}{2}(x + 2)$.

Step3: Find x - intercept (y = 0)

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

Answer:

(2, 0)