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:

Identify coordinates from the graph

Using the Slope of a Line knowledge point

$$ A = (-4, 0),\quad B = (2, -3),\quad C = (-2, 2) $$

Calculate the slope of line AB

Using the Slope of a Line knowledge point

$$ m = \frac{-3 - 0}{2 - (-4)} = \frac{-3}{6} = -\frac{1}{2} $$

Determine the parallel line equation

Using the Parallel Line Equations and Point-Slope Form knowledge points

$$
LATEXBLOCK0
$$

Find the x-axis intersection point

To find the point on the \(x\)-axis, set \(y = 0\):

$$
LATEXBLOCK1
$$

Thus, the point is \((2, 0)\).

Answer:

• (1, 0)
• (1, 1)
• (0, 2)
• (2, 0) (Correct answer)