select the correct answer from each drop - down menu. given: w(-1,1), x(3,4), y(6,0), and z(2,-3) are the vertices of quadrilateral wxyz. prove: wxyz is a square. using the distance formula, i found that drop - down menu options: all four sides have different lengths, only 2 sides have the same length, all four sides have a length of 5, all four sides have a length of 10 next

Question

Accepted Answer

# 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 $WX$
For $W(-1,1)$ and $X(3,4)$:
$$
\begin{align*}
WX&=\sqrt{(3 - (-1))^2+(4 - 1)^2}\
&=\sqrt{(4)^2+(3)^2}\
&=\sqrt{16 + 9}\
&=\sqrt{25}\
&= 5
\end{align*}
$$

## Step3: Calculate $XY$
For $X(3,4)$ and $Y(6,0)$:
$$
\begin{align*}
XY&=\sqrt{(6 - 3)^2+(0 - 4)^2}\
&=\sqrt{(3)^2+(-4)^2}\
&=\sqrt{9 + 16}\
&=\sqrt{25}\
&= 5
\end{align*}
$$

## Step4: Calculate $YZ$
For $Y(6,0)$ and $Z(2,-3)$:
$$
\begin{align*}
YZ&=\sqrt{(2 - 6)^2+(-3 - 0)^2}\
&=\sqrt{(-4)^2+(-3)^2}\
&=\sqrt{16 + 9}\
&=\sqrt{25}\
&= 5
\end{align*}
$$

## Step5: Calculate $ZW$
For $Z(2,-3)$ and $W(-1,1)$:
$$
\begin{align*}
ZW&=\sqrt{(-1 - 2)^2+(1 - (-3))^2}\
&=\sqrt{(-3)^2+(4)^2}\
&=\sqrt{9 + 16}\
&=\sqrt{25}\
&= 5
\end{align*}
$$

# Answer:
all four sides have a length of 5

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QUESTION IMAGE

Question

Explanation:

Step1: Recall Distance Formula

Step2: Calculate \(WX\)

Step3: Calculate \(XY\)

Step4: Calculate \(YZ\)

Step5: Calculate \(ZW\)

Answer: