Question

question 7/8
graph the quadrilateral on graph
paper, then answer the questions.
7 the vertices of quadrilateral pqrs are:
p(4,7) q(11,5) r(5, - 16) s( - 2, - 14)
(a)
complete the steps below to prove
whether quadrilateral pqrs is a
rectangle.
what are the slopes of each side?
pq =
rs =
qr =
ps =
(b) prove whether quadrilateral
pqrs is a rectangle. use your
answers from the first part along
with any other additional
information to support your
answer.
√x

Explanation:

Step1: Calculate slope of \(PQ\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For \(P(4,7)\) and \(Q(11,5)\), \(m_{PQ}=\frac{5 - 7}{11 - 4}=\frac{-2}{7}\).

Step2: Calculate slope of \(RS\)

For \(R(5,-16)\) and \(S(-2,-14)\), \(m_{RS}=\frac{-14+16}{-2 - 5}=\frac{2}{-7}=-\frac{2}{7}\).

Step3: Calculate slope of \(QR\)

For \(Q(11,5)\) and \(R(5,-16)\), \(m_{QR}=\frac{-16 - 5}{5 - 11}=\frac{-21}{-6}=\frac{7}{2}\).

Step4: Calculate slope of \(PS\)

For \(P(4,7)\) and \(S(-2,-14)\), \(m_{PS}=\frac{-14 - 7}{-2 - 4}=\frac{-21}{-6}=\frac{7}{2}\).

Answer:

\(PQ=-\frac{2}{7}\), \(RS =-\frac{2}{7}\), \(QR=\frac{7}{2}\), \(PS=\frac{7}{2}\)