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if quadrilateral qwer has vertices at q(0,3), w(4,0), e(7,4), and r(3,7), prove that quadrilateral qwer is a square.
use the keypad to enter the answer in the box provided. express your answers in fractions wherever possible or appropriate.
1 quadrilateral qwer has vertices at q(0,3), w(4,0), e(7,4), and r(3,7). 1. given
2 qw = units 2 distance formula
we = units

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $QW$
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 $Q(0,3)$ and $W(4,0)$, we have $x_1 = 0,y_1=3,x_2 = 4,y_2 = 0$.
$$
\begin{align*}
QW&=\sqrt{(4 - 0)^2+(0 - 3)^2}\
&=\sqrt{16 + 9}\
&=\sqrt{25}\
&=5
\end{align*}
$$
## Step2: Calculate the length of $WE$
For $W(4,0)$ and $E(7,4)$, we have $x_1 = 4,y_1=0,x_2 = 7,y_2 = 4$.
$$
\begin{align*}
WE&=\sqrt{(7 - 4)^2+(4 - 0)^2}\
&=\sqrt{9+16}\
&=\sqrt{25}\
&=5
\end{align*}
$$

# Answer:
$QW = 5$ units, $WE=5$ units

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(QW\)

Step2: Calculate the length of \(WE\)

Answer: