Question

triangle jkl is given by these coordinates: j(-8,-2), k(-6,5), and l(6,2).
dimitri claims that triangle jkl is a right triangle.
select the correct statement about dimitris claim.
a. dimitri is correct because side jk and side jl are perpendicular
b. dimitri is incorrect because none of the sides are perpendicular
c. dimitri is correct because side jl and side kl are perpendicular
d. dimitri is correct because side jk and side kl are perpendicular

Explanation:

Step1: Calculate the slopes of the sides

The formula for the slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
For side \(JK\) with \(J(-8,-2)\) and \(K(-6,5)\):
\(m_{JK}=\frac{5-(-2)}{-6 - (-8)}=\frac{5 + 2}{-6+8}=\frac{7}{2}\)
For side \(KL\) with \(K(-6,5)\) and \(L(6,2)\):
\(m_{KL}=\frac{2 - 5}{6-(-6)}=\frac{-3}{12}=-\frac{1}{4}\)
For side \(JL\) with \(J(-8,-2)\) and \(L(6,2)\):
\(m_{JL}=\frac{2-(-2)}{6-(-8)}=\frac{2 + 2}{6 + 8}=\frac{4}{14}=\frac{2}{7}\)

Step2: Check for perpendicularity

Two lines with slopes \(m_1\) and \(m_2\) are perpendicular if \(m_1\times m_2=-1\).
\(m_{JK}\times m_{JL}=\frac{7}{2}\times\frac{2}{7}=1
eq - 1\)
\(m_{JK}\times m_{KL}=\frac{7}{2}\times(-\frac{1}{4})=-\frac{7}{8}
eq - 1\)
\(m_{JL}\times m_{KL}=\frac{2}{7}\times(-\frac{1}{4})=-\frac{1}{14}
eq - 1\)

Answer:

B. Dimitri is incorrect because none of the sides are perpendicular.