identifying congruent segments in the plane
p(-6,7),q(-4,4)
w(-2,-4),x(1,-2)
y(4,2),z(5,-2)
follow the directions below.
(a) find the length of each segment.
give an exact answer (not a decimal approximation).
pq=
wx=
yz=
(b) check all statements that are true below.
□$ \overline { p q } \cong \overline { w x } $
□$ \overline { p q } \cong \overline { y z } $
□$ \overline { w x } \cong \overline { y z } $
□ none of these are true
explanation

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 segment $PQ$ with $P(-6,7)$ and $Q(-4,4)$:
$$
\begin{align*}
PQ&=\sqrt{(-4-(-6))^2+(4 - 7)^2}\
&=\sqrt{(2)^2+(-3)^2}\
&=\sqrt{4 + 9}\
&=\sqrt{13}
\end{align*}
$$
## Step2: Calculate the length of $WX$
For segment $WX$ with $W(-2,-4)$ and $X(1,-2)$:
$$
\begin{align*}
WX&=\sqrt{(1-(-2))^2+(-2-(-4))^2}\
&=\sqrt{(3)^2+(2)^2}\
&=\sqrt{9+4}\
&=\sqrt{13}
\end{align*}
$$
## Step3: Calculate the length of $YZ$
For segment $YZ$ with $Y(4,2)$ and $Z(5,-2)$:
$$
\begin{align*}
YZ&=\sqrt{(5 - 4)^2+(-2 - 2)^2}\
&=\sqrt{(1)^2+(-4)^2}\
&=\sqrt{1+16}\
&=\sqrt{17}
\end{align*}
$$

# Answer:
- $PQ=\sqrt{13}$
- $WX=\sqrt{13}$
- $YZ=\sqrt{17}$
- For part (b), since $PQ=\sqrt{13}$ and $WX=\sqrt{13}$, the statement $\overline{PQ}\cong\overline{WX}$ is true.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Use the distance formula

Step2: Calculate the length of \(WX\)

Step3: Calculate the length of \(YZ\)

Answer: