c(0,4)
d(3,2)
e(-2,1)
f(-4,-2)
solve for cd and ef, then determine if the two segments are congruent.
1 cd = √5, ef = √5. the segments are congruent.
2 cd = √5, ef = √13. the segments are not congruent.
3 cd = √13, ef = √13. the segments are congruent.
4 cd = 6, ef = 6. the segments are congruent.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $CD$
Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $C(0,4)$ and $D(3,2)$, $x_1 = 0,y_1 = 4,x_2=3,y_2 = 2$.
$$
\begin{align*}
CD&=\sqrt{(3 - 0)^2+(2 - 4)^2}\
&=\sqrt{3^2+(- 2)^2}\
&=\sqrt{9 + 4}\
&=\sqrt{13}
\end{align*}
$$
## Step2: Calculate the length of $EF$
For points $E(-2,1)$ and $F(-4,-2)$, $x_1=-2,y_1 = 1,x_2=-4,y_2=-2$.
$$
\begin{align*}
EF&=\sqrt{(-4+2)^2+(-2 - 1)^2}\
&=\sqrt{(-2)^2+(-3)^2}\
&=\sqrt{4+9}\
&=\sqrt{13}
\end{align*}
$$
## Step3: Determine congruence
Since $CD=\sqrt{13}$ and $EF=\sqrt{13}$, two segments with equal lengths are congruent.

# Answer:
3. $CD = \sqrt{13},EF=\sqrt{13}$. The segments are congruent.

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(CD\)

Step2: Calculate the length of \(EF\)

Step3: Determine congruence

Answer: