Question

question 10 (multiple choice worth 1 points)
(04 01r 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:

• The slope formula is used to prove parallelism (same slope) or perpendicularity (opposite - reciprocal slopes), not congruence.
• The mid - point formula is used to find the mid - point of a line segment, not to prove side congruence.
• The distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) is used to calculate the length of a line segment. If the lengths of opposite sides of a quadrilateral are equal (calculated using the distance formula), then the opposite sides are congruent.

Answer:

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