Question

Which statement below is true, and could be used to show that PQRS is a rectangle?

P (4, 8), Q (0, 9), R (-2, 1), S (2, 0)


A rectangle has four right angles, and m(RS) = m(QP) = -1/3 and m(QR) = m(PS) = 3. Since (-1/3)(3) = -1, the segments are perpendicular.

A rectangle has four congruent sides, and QP = PS = SR = RQ = 8.25.

A rectangle has two pairs of parallel sides, m(RS) = m(QP) = -1/4 and m(QR) = m(PS) = 4.

A rectangle has four right angles, and m(RS) = m(QP) = -1/4 and m(QR) = m(PS) = 4. Since (-1/4)(4) = -1, the segments are perpendicula

Answer 1

If you look at the 4 statements, many of them have to do with parallel sides.
So you need to check for parallelism, for example, if PQ has the same slope as RS, and PS has the same slope as QR.
Then you need to check if PQ is perpendicular to QR (product of slopes=-1).