Question

click on the graph to plot a point. click a point to delete it. 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 $overline{no}=sqrt{61}$ slope of $overline{op}=\frac{5}{6}$ length of $overline{op}=sqrt{61}$ slope of $overline{pq}=-\frac{6}{5}$ length of $overline{pq}=sqrt{61}$ 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: Assume coordinates of Q and N

Let's assume $Q(x_1,y_1)$ and $N(x_2,y_2)$. Since the lengths of $\overline{NO}=\sqrt{61}$, $\overline{OP}=\sqrt{61}$, $\overline{PQ}=\sqrt{61}$, and the slopes suggest a symmetric - like figure. If we use the distance formula for two points to find the length of $\overline{QN}$.
Let's assume without loss of generality that if we consider the relationship between the points based on the given slopes and the fact that in a rhombus all sides are equal.
The length of $\overline{QN}$ should also be $\sqrt{61}$ because in a rhombus, all four sides are of equal length.
We know that for two points $(x_1,y_1)$ and $(x_2,y_2)$, $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Since the figure has equal - length sides as indicated by the previous calculations of $\overline{NO}$, $\overline{OP}$, and $\overline{PQ}$, the length of $\overline{QN}$ is $\sqrt{61}$.

Answer:

$\sqrt{61}$