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 non - vertical lines are perpendicular if and only if the product of their slopes is - 1, which means their slopes are negative reciprocals of each other. Two non - vertical lines are parallel if their slopes are equal.

Step2: Analyze given statements

The statement "They are perpendicular because their slopes are equal" is incorrect as equal slopes mean parallel lines. The statement "They are perpendicular because their slopes are negative reciprocals" is the correct condition for perpendicular lines. The statement "They are not perpendicular because their slopes are equal" is incorrect as equal slopes imply parallelism not non - perpendicularity in a general sense. The statement "They are not perpendicular because their slopes are not negative reciprocals" is the correct non - perpendicularity condition for non - vertical lines.

Answer:

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