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.

Step2: Analyze given statements

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

Answer:

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