Question

what is the perimeter of parallelogram wxyz? √5 + √17 units 2√5 + 2√17 units 16 units 22 units w(0, -1) x(4, 0) y(3, -2) z(-1, -3)

Explanation:

Step1: Use 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 length of WX

For points $W(0, - 1)$ and $X(4,0)$, $d_{WX}=\sqrt{(4 - 0)^2+(0+1)^2}=\sqrt{16 + 1}=\sqrt{17}$.

Step3: Find length of XY

For points $X(4,0)$ and $Y(3,-2)$, $d_{XY}=\sqrt{(3 - 4)^2+(-2 - 0)^2}=\sqrt{1 + 4}=\sqrt{5}$.

Step4: Recall property of parallelogram

In parallelogram $WXYZ$, $WX = YZ$ and $XY=WZ$.

Step5: Calculate perimeter

Perimeter $P = 2d_{WX}+2d_{XY}=2\sqrt{17}+2\sqrt{5}$ units.

Answer:

$2\sqrt{5}+2\sqrt{17}$ units