Question

Triangle JKL has vertices at the following coordinates: J(2, 2), K(-1, 3), and L(-2, -1). Determine whether or not triangle JKL is a right triangle. Show all calculations for full credit.

Answer 1

$\textbf{Given:}$

$\text{Vertices are J(2,2), K(-1,3) and L(-2,-1)}$

$\textbf{To determine:}$

$\text{JKL is a right angled triangle or not}$

$\textbf{Solution:}$

$\text{First, we find the sides of the triangle JKL}$

$\mathrm{JK=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}}$

$\mathrm{JK=\sqrt{(2+1)^2+(2-3)^2}}$

$\mathrm{JK=\sqrt{3^2+(-1)^2}}$

$\mathrm{JK=\sqrt{9+1}=\sqrt{10}}$

$\mathrm{KL=\sqrt{(-1+2)^2+(3+1)^2}}$

$\mathrm{KL=\sqrt{1^2+4^2}}$

$\mathrm{KL=\sqrt{1+16}=\sqrt{17}}$

$\mathrm{JL=\sqrt{(2+2)^2+(2+1)^2}}$

$\mathrm{JL=\sqrt{4^2+3^2}}$

$\mathrm{JL=\sqrt{16+9}=\sqrt{25}=5}$

$\text{Now}$

$\mathrm{JK^2+JL^2}$

$\mathrm{=10+25}$

$\mathrm{=35}$

$\mathrm{{\neq}\;KL^2}$

$\implies\text{Sum of the square of two sides of the triangle}$

$\text{does not equal to square of the 3 rd side}$

$\therefore\textbf{Triangle JKL is not a right angled triangle}$

Find more:

points A(3,0), B(a,-2)and C(4,-1) are vertices of triangle ABC right angled at vertex A. Find value of a

https://brainly.in/question/4290807

Answer 2

Answer: not a right triangle.

Step-by-step explanation: