Question

select the correct answer from each drop - down menu.
the length of side pq is
the length of side qr is about
the perimeter of the parallelogram pqrs is about

Explanation:

Step1: Identify coordinates of P and Q

Let \(P(-5,3)\) and \(Q(-3,3)\).

Step2: Calculate length of PQ

Since \(y - \)coordinates are the same, \(PQ=\vert-3-(-5)\vert=\vert-3 + 5\vert = 2\) units.

Step3: Identify coordinates of Q and R

Let \(Q(-3,3)\) and \(R(-2,1)\).

Step4: Use distance formula for QR

The distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), so \(QR=\sqrt{(-2+3)^2+(1 - 3)^2}=\sqrt{1+( - 2)^2}=\sqrt{1 + 4}=\sqrt{5}\approx2.24\) units.

Step5: Recall properties of parallelogram

In parallelogram \(PQRS\), \(PQ = SR\) and \(QR=PS\). Perimeter \(P = 2(PQ+QR)=2(2+\sqrt{5})=4 + 2\sqrt{5}\approx4+2\times2.24=4 + 4.47=8.47\approx8.5\) units.

Answer:

The length of side PQ is 2 units.
The length of side QR is about 2.24 units.
The perimeter of the parallelogram PQRS is about 8.5 units.