given the points a (3,-2), b (2,-5), and c (4,-5), classify △abc. (1 point) it is an equilateral triangle. it is an right triangle. it is an isosceles triangle. it is an scalene triangle.

Question

Accepted Answer

# 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 side $AB$ with $A(3,-2)$ and $B(2,-5)$:
$$
\begin{align*}
AB&=\sqrt{(2 - 3)^2+(-5+ 2)^2}\
&=\sqrt{(-1)^2+(-3)^2}\
&=\sqrt{1 + 9}\
&=\sqrt{10}
\end{align*}
$$
For side $BC$ with $B(2,-5)$ and $C(4,-5)$:
$$
\begin{align*}
BC&=\sqrt{(4 - 2)^2+(-5 + 5)^2}\
&=\sqrt{(2)^2+0^2}\
&=2
\end{align*}
$$
For side $AC$ with $A(3,-2)$ and $C(4,-5)$:
$$
\begin{align*}
AC&=\sqrt{(4 - 3)^2+(-5 + 2)^2}\
&=\sqrt{(1)^2+(-3)^2}\
&=\sqrt{1+9}\
&=\sqrt{10}
\end{align*}
$$

## Step2: Analyze the side - length relationships
Since $AB=\sqrt{10}$, $BC = 2$, and $AC=\sqrt{10}$, we have $AB=AC$.

# Answer:
It is an isosceles triangle.

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QUESTION IMAGE

Question

Explanation:

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

Step2: Analyze the side - length relationships

Answer: