which statement best explains the relationship between lines fg and hj? they are perpendicular because their…

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.

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.

Answer

Explanation:

Step1: Recall slope - perpendicularity rule

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. If the slopes of two lines are equal, the lines are parallel.

Step2: Analyze the 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 correct in stating non - perpendicularity for equal slopes but is not the best explanation for perpendicularity. The fourth statement "They are not perpendicular because their slopes are not negative reciprocals" is correct in stating non - perpendicularity but is not the best explanation for perpendicularity.

Answer:

They are perpendicular because their slopes are negative reciprocals.