Question

On a coordinate plane, parallelogram P Q R S is shown. Point P is at (5, 1), point Q is at (6, 4), point R is at (3, 10), and point S is at (2, 7).
Which statement proves that PQRS is a parallelogram?

The slopes of SP and RQ are both –2 and SP = RQ = StartRoot 45 EndRoot.
The slopes of RS and QP are both 3 and SP = RQ = StartRoot 45 EndRoot.
The midpoint of RP is (4, 5 and one-half) and the slope of RP is Negative nine-halves.
The midpoint of SQ is (4, 5 and one-half) and SQ = 5.

Answer 1

Based on the properties of a parallelogram, the statement that proves that PQRS is a parallelogram is: A. The slopes of SP = RQ = –2, and SP = RQ = √45

What is a Parallelogram?

The opposite sides of a parallelogram are congruent and parallel. Their slopes are also the same.

Slope of SP = change in y / change in x = (7 - 1)/(2 - 5) = 6/-3 = -2

Slope of RQ = change in y / change in x = (10 - 4) / (3 - 6) = 6/-3 = -2

Therefore, the statement that is proves PQRS is a parallelogram is:

A. The slopes of SP = RQ = –2, and SP = RQ = √45

Learn more about parallelogram on:

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Answer 2

Answer: A. The slopes of SP and RQ are both –2 and SP = RQ = StartRoot 45 EndRoot.

Step-by-step explanation: On Edge!