Question

find the desired slopes and lengths, then fill in the words that best identifies the type of quadrilateral. answer attempt 1 out of 2 slope of $overline{no}=-\frac{6}{5}$ length of $overline{no}=$ slope of $overline{op}=$ length of $overline{op}=$

Explanation:

Step1: Recall slope formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For length, we use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Assume the coordinates of points $N(x_{N},y_{N})$, $O(x_{O},y_{O})$ and $P(x_{P},y_{P})$ can be read from the graph. Since the slope of $\overline{NO}=-\frac{6}{5}$, we need to find the slope of $\overline{OP}$ and lengths.

Step2: Calculate slope of $\overline{OP}$

Let's assume we know the coordinates of $O$ and $P$. If $O(x_1,y_1)$ and $P(x_2,y_2)$, then the slope of $\overline{OP}=\frac{y_2 - y_1}{x_2 - x_1}$.

Step3: Calculate length of $\overline{NO}$

If $N(x_{N},y_{N})$ and $O(x_{O},y_{O})$, then the length of $\overline{NO}=\sqrt{(x_{N}-x_{O})^2+(y_{N}-y_{O})^2}$.

Step4: Calculate length of $\overline{OP}$

If $O(x_1,y_1)$ and $P(x_2,y_2)$, then the length of $\overline{OP}=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Answer:

Since we don't have the actual coordinates of the points $N$, $O$ and $P$ from the graph, we can't give numerical values. But the general - form for slope of $\overline{OP}$ is $\frac{y_{P}-y_{O}}{x_{P}-x_{O}}$ and length of $\overline{NO}$ is $\sqrt{(x_{N}-x_{O})^2+(y_{N}-y_{O})^2}$, length of $\overline{OP}$ is $\sqrt{(x_{P}-x_{O})^2+(y_{P}-y_{O})^2}$