Question

which statement best explains the relationship between lines cd and fg?
○ they are perpendicular because their slopes are equal.
○ they are perpendicular because their slopes are negative reciprocals.
○ they are not perpendicular because their slopes are equal.
○ they are not perpendicular because their slopes are negative reciprocals.

Explanation:

Step1: Find coordinates of points for line CD

Points on line CD: C(-2, 4) and D(0, -4)
Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
Slope of CD: $\frac{-4 - 4}{0 - (-2)} = \frac{-8}{2} = -4$

Step2: Find coordinates of points for line FG

Points on line FG: F(-4, 0) and G(4, 2)
Slope of FG: $\frac{2 - 0}{4 - (-4)} = \frac{2}{8} = \frac{1}{4}$

Step3: Check relationship of slopes

Two lines are perpendicular if slopes are negative reciprocals (product = -1).
Product of slopes: $-4 \times \frac{1}{4} = -1$
So slopes are negative reciprocals, meaning lines are perpendicular.

Answer:

They are perpendicular because their slopes are negative reciprocals. (The option: They are perpendicular because their slopes are negative reciprocals.)