Question

question 5(multiple choice worth 1 points) (04.01 lc) which statement explains how you could use coordinate geometry to prove the opposite sides of a quadrilateral are congruent? use the slope formula to prove the slopes of the opposite sides are the same. use the slope formula to prove the slopes of the opposite sides are opposite reciprocals. use the distance formula to prove the lengths of the opposite sides are the same. use the distance formula to prove the midpoints of the opposite sides are the same.

Explanation:

Step1: Recall congruence definition

Two line - segments (sides of quadrilateral) are congruent if they have equal lengths.

Step2: Analyze each option

• Option A: Using slope formula to prove slopes of opposite sides are the same shows parallel sides, not congruent sides.
• Option B: Proving slopes of opposite sides are opposite reciprocals shows perpendicular sides, not congruent sides.
• Option C: The distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ is used to find the length of a line - segment between two points. If the lengths of opposite sides of a quadrilateral are equal using this formula, then the opposite sides are congruent.
• Option D: Using the distance formula to prove mid - points of opposite sides are the same is incorrect. The mid - point formula is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$, and mid - points being the same is not related to side lengths being congruent.

Answer:

C. Use the distance formula to prove the lengths of the opposite sides are the same.