Question

1. which statements describe the sides of the parallelogram below? select all that apply. sides $overline{pq}$ and $overline{rs}$ both have a slope of 2. sides $overline{pq}$ and $overline{rs}$ are both $sqrt{80}$ units. sides $overline{qr}$ and $overline{sp}$ both have a slope of - 1.5. sides $overline{qr}$ and $overline{sp}$ are both $sqrt{74}$ units.

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Find coordinates of points

Let's assume $P(- 5,7)$, $Q(-1,15)$, $R(5,8)$ and $S(0,0)$.

Step3: Calculate slope of $PQ$

$m_{PQ}=\frac{15 - 7}{-1-(-5)}=\frac{8}{4}=2$.

Step4: Calculate slope of $RS$

$m_{RS}=\frac{8 - 0}{5 - 0}=\frac{8}{5}
eq2$.

Step5: Calculate length of $PQ$ using distance formula

The distance formula is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $PQ$ with $x_1=-5,y_1 = 7,x_2=-1,y_2 = 15$, $d_{PQ}=\sqrt{(-1+5)^2+(15 - 7)^2}=\sqrt{4^2+8^2}=\sqrt{16 + 64}=\sqrt{80}$.

Step6: Calculate length of $RS$

For $RS$ with $x_1 = 0,y_1=0,x_2 = 5,y_2 = 8$, $d_{RS}=\sqrt{(5 - 0)^2+(8 - 0)^2}=\sqrt{25+64}=\sqrt{89}
eq\sqrt{80}$.

Step7: Calculate slope of $QR$

$m_{QR}=\frac{8 - 15}{5+1}=\frac{-7}{6}
eq - 1.5$.

Step8: Calculate slope of $SP$

$m_{SP}=\frac{7-0}{-5 - 0}=-\frac{7}{5}
eq-1.5$.

Step9: Calculate length of $QR$

For $QR$ with $x_1=-1,y_1 = 15,x_2 = 5,y_2 = 8$, $d_{QR}=\sqrt{(5 + 1)^2+(8 - 15)^2}=\sqrt{36+49}=\sqrt{85}
eq\sqrt{74}$.

Step10: Calculate length of $SP$

For $SP$ with $x_1=-5,y_1 = 7,x_2 = 0,y_2 = 0$, $d_{SP}=\sqrt{(0 + 5)^2+(0 - 7)^2}=\sqrt{25 + 49}=\sqrt{74}$.

The only correct statement is that sides $\overline{PQ}$ and $\overline{RS}$ are both $\sqrt{80}$ units.

Answer:

Sides $\overline{PQ}$ and $\overline{RS}$ are both $\sqrt{80}$ units.