Question

determine the perimeter of the given figure on the coordinate plane. round your answer to the nearest hundredth, if necessary. parallelogram w x y z

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: Assume coordinates

Let's assume $W(4,6)$, $X(6,8)$, $Y(8,5)$, $Z(6,3)$.

Step3: Calculate length of $WX$

$d_{WX}=\sqrt{(6 - 4)^2+(8 - 6)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\approx2.83$.

Step4: Calculate length of $XY$

$d_{XY}=\sqrt{(8 - 6)^2+(5 - 8)^2}=\sqrt{4 + 9}=\sqrt{13}\approx3.61$.

Step5: Calculate perimeter of parallelogram

In a parallelogram, opposite sides are equal. So perimeter $P = 2(d_{WX}+d_{XY})=2(2\sqrt{2}+\sqrt{13})\approx2(2.83 + 3.61)=2\times6.44 = 12.88$.

Answer:

$12.88$