we know that
The formula to calculate the slope between two points is equal to
![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
we have
![J(-5,-1)\ K(0,1)\ L(2,-5)](https://tex.z-dn.net/?f=J%28-5%2C-1%29%5C%20K%280%2C1%29%5C%20L%282%2C-5%29)
Step 1
Find the slope of the side JK
![J(-5,-1)\ K(0,1)](https://tex.z-dn.net/?f=J%28-5%2C-1%29%5C%20K%280%2C1%29)
substitute the values in the formula
![m=\frac{1+1}{0+5}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%2B1%7D%7B0%2B5%7D)
![mJK=\frac{2}{5}](https://tex.z-dn.net/?f=mJK%3D%5Cfrac%7B2%7D%7B5%7D)
Step 2
Find the slope of the side KL
![K(0,1)\ L(2,-5)](https://tex.z-dn.net/?f=K%280%2C1%29%5C%20L%282%2C-5%29)
substitute the values in the formula
![m=\frac{-5-1}{2-0}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-5-1%7D%7B2-0%7D)
![m=\frac{-6}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-6%7D%7B2%7D)
![mKL=-3](https://tex.z-dn.net/?f=mKL%3D-3)
Step 3
Find the slope of the side JL
![J(-5,-1)\ L(2,-5)](https://tex.z-dn.net/?f=J%28-5%2C-1%29%5C%20L%282%2C-5%29)
substitute the values in the formula
![m=\frac{-5+1}{2+5}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-5%2B1%7D%7B2%2B5%7D)
![m=\frac{-4}{7}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-4%7D%7B7%7D)
![mJL=-\frac{4}{7}](https://tex.z-dn.net/?f=mJL%3D-%5Cfrac%7B4%7D%7B7%7D)
Step 4
Verify if triangle JKL is a right triangle
we know that
if two lines are perpendicular, then the product of their slopes is equal to minus one
so
![m1*m2=-1](https://tex.z-dn.net/?f=m1%2Am2%3D-1)
a) compare slope JK with slope KL
we have
![mJK=\frac{2}{5}](https://tex.z-dn.net/?f=mJK%3D%5Cfrac%7B2%7D%7B5%7D)
![mKL=-3](https://tex.z-dn.net/?f=mKL%3D-3)
![\frac{2}{5}*-3=-\frac{6}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D%2A-3%3D-%5Cfrac%7B6%7D%7B5%7D)
-------> the side JK and side KL are not perpendicular
b) compare slope KL with slope JL
we have
![mKL=-3](https://tex.z-dn.net/?f=mKL%3D-3)
![mJL=-\frac{4}{7}](https://tex.z-dn.net/?f=mJL%3D-%5Cfrac%7B4%7D%7B7%7D)
![-\frac{4}{7}*-3=\frac{12}{7}](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B7%7D%2A-3%3D%5Cfrac%7B12%7D%7B7%7D)
-------> the side KL and side JL are not perpendicular
c) compare slope JK with slope JL
we have
![mJK=\frac{2}{5}](https://tex.z-dn.net/?f=mJK%3D%5Cfrac%7B2%7D%7B5%7D)
![mJL=-\frac{4}{7}](https://tex.z-dn.net/?f=mJL%3D-%5Cfrac%7B4%7D%7B7%7D)
![-\frac{4}{7}*\frac{2}{5}=-\frac{8}{35}](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B7%7D%2A%5Cfrac%7B2%7D%7B5%7D%3D-%5Cfrac%7B8%7D%7B35%7D)
-------> the side JK and side JL are not perpendicular
therefore
<u>the answer is</u>
The triangle JKL is not a right triangle