on a grid, draw the triangle with each set of vertices. then classify the triangle as scalene, isosceles, or equilateral.
a) a(-5, 5), b(2, 1), c(-6, 0)
b) g(-2, -3), h(9, 1), j(7, 7)

Question

Accepted Answer

# Explanation:
## Step1: Recall distance formula
The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
## Step2: Calculate side - length AB
For points $A(-5,5)$ and $B(2,1)$, we have $x_1=-5,y_1 = 5,x_2=2,y_2 = 1$.
$$
\begin{align*}
AB&=\sqrt{(2+5)^2+(1 - 5)^2}\
&=\sqrt{7^2+( - 4)^2}\
&=\sqrt{49 + 16}\
&=\sqrt{65}
\end{align*}
$$
## Step3: Calculate side - length BC
For points $B(2,1)$ and $C(-6,6)$, we have $x_1=2,y_1 = 1,x_2=-6,y_2 = 6$.
$$
\begin{align*}
BC&=\sqrt{(-6 - 2)^2+(6 - 1)^2}\
&=\sqrt{(-8)^2+5^2}\
&=\sqrt{64 + 25}\
&=\sqrt{89}
\end{align*}
$$
## Step4: Calculate side - length AC
For points $A(-5,5)$ and $C(-6,6)$, we have $x_1=-5,y_1 = 5,x_2=-6,y_2 = 6$.
$$
\begin{align*}
AC&=\sqrt{(-6 + 5)^2+(6 - 5)^2}\
&=\sqrt{(-1)^2+1^2}\
&=\sqrt{1+1}\
&=\sqrt{2}
\end{align*}
$$
Since $AB
eq BC
eq AC$, the triangle is scalene.

# Answer:
The triangle with vertices $A(-5,5)$, $B(2,1)$ and $C(-6,6)$ is scalene.

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QUESTION IMAGE

Question

Explanation:

Step1: Recall distance formula

Step2: Calculate side - length AB

Step3: Calculate side - length BC

Step4: Calculate side - length AC

Answer: