Question

which statement best explains the relationship between lines fg and hj?
○ 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 not negative reciprocals.

Explanation:

Step1: Find slope of HJ

Points on HJ: H(-4, -2), J(0, 4). Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$. So $m_{HJ} = \frac{4 - (-2)}{0 - (-4)} = \frac{6}{4} = \frac{3}{2}$.

Step2: Find slope of FG

Points on FG: F(-4, 1), G(0, -2). Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$. So $m_{FG} = \frac{-2 - 1}{0 - (-4)} = \frac{-3}{4}$.

Step3: Check perpendicularity

Perpendicular slopes are negative reciprocals (product = -1). $\frac{3}{2} \times \frac{-3}{4} = \frac{-9}{8}
eq -1$. So slopes aren't negative reciprocals, so not perpendicular.

Answer:

They are not perpendicular because their slopes are not negative reciprocals. (The option: They are not perpendicular because their slopes are not negative reciprocals.)