if $ \triangle a b c \cong \triangle e d f $ where the coordinates of $ a(-1,1), b(2,4) $, and $ c(3,1) $, what is the measure of $ e f $ ? (1 point)
3
3.2
4
4.6

Question

Accepted Answer

# Explanation:
## Step1: Use the distance formula
The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $\triangle ABC\cong\triangle EDF$, $EF = BC$.
## Step2: Calculate the length of $BC$
Given $B(2,4)$ and $C(3,1)$, substitute $x_1 = 2,y_1 = 4,x_2 = 3,y_2 = 1$ into the distance formula:
$$
\begin{align*}
BC&=\sqrt{(3 - 2)^2+(1 - 4)^2}\
&=\sqrt{1^2+(- 3)^2}\
&=\sqrt{1 + 9}\
&=\sqrt{10}\approx3.2
\end{align*}
$$

# Answer:
$3.2$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the distance formula

Step2: Calculate the length of \(BC\)

Answer: