directions: find the measures of the sides of $ riangle jkl$, then classify it by its sides.
21. $j(-7,-7),k(-9,1),l(-1,-1)$
22. $j(-3,2),k(2,6),l(8,-1)$
23. $j(1,-13),k(3,3),l(10,-6)$
24. $j(7,-2),k(-4,9),l(-3,-1)$

Question

directions: find the measures of the sides of $	riangle jkl$, then classify it by its sides.
21. $j(-7,-7),k(-9,1),l(-1,-1)$
22. $j(-3,2),k(2,6),l(8,-1)$
23. $j(1,-13),k(3,3),l(10,-6)$
24. $j(7,-2),k(-4,9),l(-3,-1)$

Accepted Answer

# Explanation:
## Step1: Calculate the length of $JK$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
For $J(-3,2)$ and $K(2,6)$, $x_1=-3,y_1 = 2,x_2=2,y_2=6$
$$
\begin{align*}
JK&=\sqrt{(2-(-3))^2+(6 - 2)^2}\
&=\sqrt{(2 + 3)^2+(6 - 2)^2}\
&=\sqrt{5^2+4^2}\
&=\sqrt{25 + 16}\
&=\sqrt{41}
\end{align*}
$$
## Step2: Calculate the length of $KL$
For $K(2,6)$ and $L(8,-1)$, $x_1=2,y_1 = 6,x_2=8,y_2=-1$
$$
\begin{align*}
KL&=\sqrt{(8 - 2)^2+(-1 - 6)^2}\
&=\sqrt{6^2+(-7)^2}\
&=\sqrt{36+49}\
&=\sqrt{85}
\end{align*}
$$
## Step3: Calculate the length of $JL$
For $J(-3,2)$ and $L(8,-1)$, $x_1=-3,y_1 = 2,x_2=8,y_2=-1$
$$
\begin{align*}
JL&=\sqrt{(8-(-3))^2+(-1 - 2)^2}\
&=\sqrt{(8 + 3)^2+(-3)^2}\
&=\sqrt{11^2+(-3)^2}\
&=\sqrt{121+9}\
&=\sqrt{130}
\end{align*}
$$
Since $JK=\sqrt{41}$, $KL=\sqrt{85}$, $JL=\sqrt{130}$ and all sides are of different lengths.

# Answer:
Side Measures: $JK=\sqrt{41}$, $KL=\sqrt{85}$, $JL=\sqrt{130}$; Type of Triangle: Scalene triangle

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(JK\)

Step2: Calculate the length of \(KL\)

Step3: Calculate the length of \(JL\)

Answer: