Question

find the desired slopes and lengths, then fill in the words that best identifies the type of quadrilateral. answer attempt 2 out of 2 slope of $overline{no}=-\frac{6}{5}$ length of $overline{no}=$ slope of $overline{op}=\frac{5}{6}$ length of $overline{op}=sqrt{61}$ slope of $overline{pq}=-\frac{6}{5}$ length of $overline{pq}=$ slope of $overline{qn}=\frac{5}{6}$ length of $overline{qn}=$ quadrilateral nopq can best be described as

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Find length of $\overline{NO}$

Let the coordinates of $N$ be $(x_1,y_1)$ and of $O$ be $(x_2,y_2)$. Assume $N=(6,1)$ and $O=(1,7)$. Then $d_{NO}=\sqrt{(1 - 6)^2+(7 - 1)^2}=\sqrt{(- 5)^2+6^2}=\sqrt{25 + 36}=\sqrt{61}$.

Step3: Find length of $\overline{PQ}$

Assume $P=(-3,4)$ and $Q=(2,-2)$. Then $d_{PQ}=\sqrt{(2+3)^2+(-2 - 4)^2}=\sqrt{5^2+(-6)^2}=\sqrt{25 + 36}=\sqrt{61}$.

Step4: Find length of $\overline{QN}$

Assume $Q=(2,-2)$ and $N=(6,1)$. Then $d_{QN}=\sqrt{(6 - 2)^2+(1 + 2)^2}=\sqrt{4^2+3^2}=\sqrt{16 + 9}=\sqrt{25}=5$.

Answer:

length of $\overline{NO}=\sqrt{61}$
length of $\overline{PQ}=\sqrt{61}$
length of $\overline{QN}=5$