Question

select the correct answer from each drop - down menu. find the approximate side lengths and perimeter of quadrilateral wxyz. if necessary, round your answers to the nearest hundredth. the approximate length of segment wx is units. the approximate length of segment xy is units. the approximate length of segment yz is units. the approximate perimeter of quadrilateral wxyz is units.

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: Find coordinates of points

From the graph, assume $W(3,1)$, $X(7, - 1)$, $Y(7,-3)$, $Z(3,-3)$.

Step3: Calculate length of WX

For points $W(3,1)$ and $X(7,-1)$:
$d_{WX}=\sqrt{(7 - 3)^2+(-1 - 1)^2}=\sqrt{4^2+(-2)^2}=\sqrt{16 + 4}=\sqrt{20}\approx4.47$.

Step4: Calculate length of XY

For points $X(7,-1)$ and $Y(7,-3)$:
$d_{XY}=\sqrt{(7 - 7)^2+(-3+1)^2}=\sqrt{0^2+(-2)^2}=2$.

Step5: Calculate length of YZ

For points $Y(7,-3)$ and $Z(3,-3)$:
$d_{YZ}=\sqrt{(3 - 7)^2+(-3 + 3)^2}=\sqrt{(-4)^2+0^2}=4$.

Step6: Calculate perimeter

Perimeter $P=d_{WX}+d_{XY}+d_{YZ}+d_{ZW}$. Since $ZW$ has the same length as $XY$ (by symmetry), $P\approx4.47+2 + 4+2=12.47$.

Answer:

The approximate length of segment WX is $4.47$ units.
The approximate length of segment XY is $2$ units.
The approximate length of segment YZ is $4$ units.
The approximate perimeter of quadrilateral WXYZ is $12.47$ units.