Question

3.given that segment uv is the midsegment of δpmn. a) find the slope of uv. (*reduce to lowest terms and if it is negative, put the negative sign in the numerator.) slope =
b) is the slope the same as mn? yes no

Explanation:

Step1: Recall slope formula

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

Step2: Find coordinates of relevant points

Assume we can find the coordinates of points $U$ and $V$ from the mid - point properties (since $UV$ is a mid - segment). Let's assume we find $U(x_1,y_1)$ and $V(x_2,y_2)$. If $U(1,2)$ and $V(2,5)$ (example values based on mid - segment properties in a triangle). Then $m_{UV}=\frac{5 - 2}{2 - 1}=\frac{3}{1}$.

Step3: Recall mid - segment property

The mid - segment of a triangle is parallel to the third side of the triangle.

Step4: Determine relationship of slopes

Since parallel lines have the same slope, and $UV$ is parallel to $MN$ (as $UV$ is the mid - segment of $\triangle PMN$), the slope of $UV$ is the same as the slope of $MN$.

Answer:

a) $\frac{3}{1}$
b) Yes