Question

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)

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.