Question

j(2, 1) m(3, 2) l(7, 2) k(2, - 3) rhombus parallelogram trapezoid isosceles trapezoid

Explanation:

Step1: Recall the slope - formula

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

Step2: Calculate the slope of JM

For points $J(2,1)$ and $M(3,2)$, $m_{JM}=\frac{2 - 1}{3 - 2}=1$.

Step3: Calculate the slope of ML

For points $M(3,2)$ and $L(7,2)$, $m_{ML}=\frac{2 - 2}{7 - 3}=0$.

Step4: Calculate the slope of LK

For points $L(7,2)$ and $K(2,-3)$, $m_{LK}=\frac{-3 - 2}{2 - 7}=\frac{-5}{-5}=1$.

Step5: Calculate the slope of KJ

For points $K(2,-3)$ and $J(2,1)$, $m_{KJ}=\frac{1+3}{2 - 2}$, which is undefined (vertical line).

Step6: Analyze the properties of the quadrilateral

Since $m_{JM}=m_{LK}=1$ and $m_{ML}=0$, $m_{KJ}$ is undefined, one pair of opposite sides is parallel. A quadrilateral with one pair of opposite sides parallel is a trapezoid.

Answer:

trapezoid