Question

select the correct answer from each drop - down menu. wxyz is a quadrilateral graphed in the coordinate plane with vertices w(0,5), x(-3,2), y(0,-4), and z(3,2). what are the lengths of the sides of the quadrilateral, and what is the correct name for the figure? the length of (overline{wx}) is about <6.71>. the length of (overline{xy}) is about <4.24>. the length of (overline{yz}) is about <3.46>. the length of (overline{zw}) is about <8.66>. the best name for this quad

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 length of $\overline{WX}$

For points $W(0,5)$ and $X(-3,2)$, $x_1 = 0,y_1 = 5,x_2=-3,y_2 = 2$. Then $d_{WX}=\sqrt{(-3 - 0)^2+(2 - 5)^2}=\sqrt{(-3)^2+(-3)^2}=\sqrt{9 + 9}=\sqrt{18}\approx4.24$.

Step3: Calculate length of $\overline{XY}$

For points $X(-3,2)$ and $Y(0,-4)$, $x_1=-3,y_1 = 2,x_2 = 0,y_2=-4$. Then $d_{XY}=\sqrt{(0+3)^2+(-4 - 2)^2}=\sqrt{3^2+(-6)^2}=\sqrt{9 + 36}=\sqrt{45}\approx6.71$.

Step4: Calculate length of $\overline{YZ}$

For points $Y(0,-4)$ and $Z(3,2)$, $x_1 = 0,y_1=-4,x_2 = 3,y_2 = 2$. Then $d_{YZ}=\sqrt{(3 - 0)^2+(2 + 4)^2}=\sqrt{3^2+6^2}=\sqrt{9+36}=\sqrt{45}\approx6.71$.

Step5: Calculate length of $\overline{ZW}$

For points $Z(3,2)$ and $W(0,5)$, $x_1 = 3,y_1 = 2,x_2 = 0,y_2 = 5$. Then $d_{ZW}=\sqrt{(0 - 3)^2+(5 - 2)^2}=\sqrt{(-3)^2+3^2}=\sqrt{9 + 9}=\sqrt{18}\approx4.24$.
Since opposite - sides are equal ($WX = ZW\approx4.24$ and $XY = YZ\approx6.71$), the quadrilateral is a parallelogram.

Answer:

The length of $\overline{WX}$ is about $4.24$. The length of $\overline{XY}$ is about $6.71$. The length of $\overline{YZ}$ is about $6.71$. The length of $\overline{ZW}$ is about $4.24$. The best name for this quadrilateral is parallelogram.