Question

directions: find the measures of the sides of \\( \triangle j k l \\), then classify it by its sides.

1. \\( j(-7,-7), k(-9,1), l(-1,-1) \\)
2. \\( j(-3,2), k(2,6), l(8,-1) \\)
3. \\( j(1,-13), k(3,3), l(10,-6) \\)
4. \\( j(7,-2), k(-4,9), l(-3,-1) \\)

Explanation:

Step1: Calculate the length of \(JK\)

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(J(1,-13)\) and \(K(3,3)\), \(x_1 = 1,y_1=-13,x_2 = 3,y_2 = 3\).
\(JK=\sqrt{(3 - 1)^2+(3+ 13)^2}=\sqrt{2^2+16^2}=\sqrt{4 + 256}=\sqrt{260}=2\sqrt{65}\)

Step2: Calculate the length of \(KL\)

For \(K(3,3)\) and \(L(10,-6)\), \(x_1 = 3,y_1 = 3,x_2 = 10,y_2=-6\).
\(KL=\sqrt{(10 - 3)^2+(-6 - 3)^2}=\sqrt{7^2+(-9)^2}=\sqrt{49+81}=\sqrt{130}\)

Step3: Calculate the length of \(JL\)

For \(J(1,-13)\) and \(L(10,-6)\), \(x_1 = 1,y_1=-13,x_2 = 10,y_2=-6\).
\(JL=\sqrt{(10 - 1)^2+(-6 + 13)^2}=\sqrt{9^2+7^2}=\sqrt{81 + 49}=\sqrt{130}\)

Step1: Calculate the length of \(JK\)

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(J(7,-2)\) and \(K(-4,9)\), \(x_1 = 7,y_1=-2,x_2=-4,y_2 = 9\).
\(JK=\sqrt{(-4 - 7)^2+(9 + 2)^2}=\sqrt{(-11)^2+11^2}=\sqrt{121+121}=\sqrt{242}=11\sqrt{2}\)

Step2: Calculate the length of \(KL\)

For \(K(-4,9)\) and \(L(-3,-1)\), \(x_1=-4,y_1 = 9,x_2=-3,y_2=-1\).
\(KL=\sqrt{(-3 + 4)^2+(-1 - 9)^2}=\sqrt{1^2+(-10)^2}=\sqrt{1 + 100}=\sqrt{101}\)

Step3: Calculate the length of \(JL\)

For \(J(7,-2)\) and \(L(-3,-1)\), \(x_1 = 7,y_1=-2,x_2=-3,y_2=-1\).
\(JL=\sqrt{(-3 - 7)^2+(-1 + 2)^2}=\sqrt{(-10)^2+1^2}=\sqrt{100 + 1}=\sqrt{101}\)

Answer:

\(JK = 2\sqrt{65}\), \(KL=\sqrt{130}\), \(JL=\sqrt{130}\); Isosceles triangle