Question

graph the quadrilateral on graph paper, then answer the questions.
7 the vertices of quadrilateral pqrs are:
p(5,4) q(9, - 1) r(-6, - 13) s(-10, - 8)
(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.

Explanation:

Step1: Calculate slope of \(PQ\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For \(P(5,4)\) and \(Q(9,-1)\), \(m_{PQ}=\frac{-1 - 4}{9 - 5}=\frac{-5}{4}\)

Step2: Calculate slope of \(RS\)

For \(R(-6,-13)\) and \(S(-10,-8)\), \(m_{RS}=\frac{-8+13}{-10 + 6}=\frac{5}{-4}=-\frac{5}{4}\)

Step3: Calculate slope of \(QR\)

For \(Q(9,-1)\) and \(R(-6,-13)\), \(m_{QR}=\frac{-13 + 1}{-6 - 9}=\frac{-12}{-15}=\frac{4}{5}\)

Step4: Calculate slope of \(PS\)

For \(P(5,4)\) and \(S(-10,-8)\), \(m_{PS}=\frac{-8 - 4}{-10 - 5}=\frac{-12}{-15}=\frac{4}{5}\)

Answer:

\(PQ=-\frac{5}{4}\), \(RS =-\frac{5}{4}\), \(QR=\frac{4}{5}\), \(PS=\frac{4}{5}\)