Question

classify each triangle as scalene, isosceles, or equilateral. determine whether the triangle is a right triangle.

1. j(-7, -7), k(-9, 1), l(-1, -1)
2. j(-3, 2), k(2, 6), l(8, -1)

Explanation:

Step1: Calculate the lengths of the sides using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

For \(JK\) with \(J(-7,-7)\) and \(K(-9,1)\):
\(JK=\sqrt{(-9 + 7)^2+(1 + 7)^2}=\sqrt{(-2)^2+8^2}=\sqrt{4 + 64}=\sqrt{68}=2\sqrt{17}\)
For \(KL\) with \(K(-9,1)\) and \(L(-1,-1)\):
\(KL=\sqrt{(-1 + 9)^2+(-1 - 1)^2}=\sqrt{8^2+(-2)^2}=\sqrt{64 + 4}=\sqrt{68}=2\sqrt{17}\)
For \(JL\) with \(J(-7,-7)\) and \(L(-1,-1)\):
\(JL=\sqrt{(-1 + 7)^2+(-1 + 7)^2}=\sqrt{6^2+6^2}=\sqrt{36+36}=\sqrt{72}=6\sqrt{2}\)

Step2: Check for triangle type

Since \(JK = KL=2\sqrt{17}\), the triangle is isosceles.

Step3: Check for right - triangle using Pythagoras theorem \(a^{2}+b^{2}=c^{2}\)

\((2\sqrt{17})^{2}+(2\sqrt{17})^{2}=68 + 68=136\) and \((6\sqrt{2})^{2}=72\), \(136
eq72\)

Answer:

The triangle is isosceles and not a right triangle.