Question

the coordinates of the vertices of \\( \triangle j k l \\) are \\( j(0,2), k(3,1) \\), and \\( l(1,-5) \\) drag and drop the choices into each box to correctly complete the sentences the slope of \\( \overline{j k} \\) is the slope of \\( \overline{k l} \\) is and the slope of \\( \overline{j l} \\) is \\( \triangle j k l \\) a right triangle because

Explanation:

Step1: Calculate the slope of $\overline{JK}$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $J(0,2)$ and $K(3,1)$, $m_{JK}=\frac{1 - 2}{3 - 0}=-\frac{1}{3}$.

Step2: Calculate the slope of $\overline{KL}$

For points $K(3,1)$ and $L(1,-5)$, $m_{KL}=\frac{-5 - 1}{1 - 3}=\frac{-6}{-2}=3$.

Step3: Calculate the slope of $\overline{JL}$

For points $J(0,2)$ and $L(1,-5)$, $m_{JL}=\frac{-5 - 2}{1 - 0}=-7$.

Step4: Check if it's a right - triangle

Two lines are perpendicular if the product of their slopes is $-1$. $(-\frac{1}{3})\times3=-1$? No, $(-\frac{1}{3})\times(-7)=\frac{7}{3}
eq - 1$, $3\times(-7)=-21
eq - 1$.

Answer:

The slope of $\overline{JK}$ is $-\frac{1}{3}$, the slope of $\overline{KL}$ is $3$, the slope of $\overline{JL}$ is $-7$, $\triangle JKL$ is not a right triangle because no two of these slopes have a product of $-1$.