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: Recall slope - perpendicularity relationship

Two lines are perpendicular if and only if the product of their slopes is - 1, i.e., their slopes are negative reciprocals of each other. If the slopes of two lines are equal, the lines are parallel.

Step2: Analyze the given statements

The first statement "They are perpendicular because their slopes are equal" is incorrect as equal - slope lines are parallel. The second statement "They are perpendicular because their slopes are negative reciprocals" would be correct for perpendicular lines. The third statement "They are not perpendicular because their slopes are equal" is incorrect as equal - slope lines are parallel, not perpendicular. The fourth statement "They are not perpendicular because their slopes are not negative reciprocals" is the correct explanation for non - perpendicular lines.

Answer:

They are not perpendicular because their slopes are not negative reciprocals.