Question

the coordinates of the vertices of quadrilateral jklm are j(-4, 1), k(2, 3), l(5, -3), and m(0, -5). drag and drop the choices into each box to correctly complete the sentences. the slope for $overline{jk}$ is, the slope of $overline{lk}$ is, the slope of $overline{ml}$ is, and the slope of $overline{mj}$ is. quadrilateral jklm a parallelogram because

Explanation:

Step1: Recall slope formula

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

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

For points $J(-4,1)$ and $K(2,3)$, $m_{JK}=\frac{3 - 1}{2-(-4)}=\frac{2}{6}=\frac{1}{3}$.

Step3: Calculate slope of $\overline{LK}$

For points $L(5,-3)$ and $K(2,3)$, $m_{LK}=\frac{3-(-3)}{2 - 5}=\frac{6}{-3}=- 2$.

Step4: Calculate slope of $\overline{ML}$

For points $M(0,-5)$ and $L(5,-3)$, $m_{ML}=\frac{-3-(-5)}{5 - 0}=\frac{2}{5}$.

Step5: Calculate slope of $\overline{MJ}$

For points $M(0,-5)$ and $J(-4,1)$, $m_{MJ}=\frac{1-(-5)}{-4 - 0}=\frac{6}{-4}=-\frac{3}{2}$.

Step6: Determine if it's a parallelogram

A quadrilateral is a parallelogram if opposite - sides are parallel (have equal slopes). Here, the slopes of opposite sides are not equal.

Answer:

The slope for $\overline{JK}$ is $\frac{1}{3}$, the slope of $\overline{LK}$ is $-2$, the slope of $\overline{ML}$ is $\frac{2}{5}$, and the slope of $\overline{MJ}$ is $-\frac{3}{2}$. Quadrilateral $JKLM$ is not a parallelogram because the slopes of opposite sides are not equal.