Question

what is the perimeter of kite wxyz? 2√53 + 2 units 2√53 + 5 units 2√53 + 10 units 2√53 + 14 units

Explanation:

Step1: Calculate length of WX

W(-3,3) and X(2,3) have the same y - coordinate. Use the distance formula for points with same y - value $d=\vert x_2 - x_1\vert$. So, $WX=\vert2-(-3)\vert = 5$.

Step2: Calculate length of ZW

W(-3,3) and Z(-3,-2) have the same x - coordinate. Use the distance formula for points with same x - value $d=\vert y_2 - y_1\vert$. So, $ZW=\vert3 - (-2)\vert=5$.

Step3: Calculate length of XY

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $X(2,3)$ and $Y(4,-4)$. Then $XY=\sqrt{(4 - 2)^2+(-4 - 3)^2}=\sqrt{2^2+(-7)^2}=\sqrt{4 + 49}=\sqrt{53}$.

Step4: Calculate length of YZ

Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $Y(4,-4)$ and $Z(-3,-2)$. Then $YZ=\sqrt{(-3 - 4)^2+(-2+4)^2}=\sqrt{(-7)^2+2^2}=\sqrt{49 + 4}=\sqrt{53}$.

Step5: Calculate the perimeter

The perimeter $P$ of the kite is $P = 2XY+2WX=2\sqrt{53}+2\times5=2\sqrt{53}+10$.

Answer:

$2\sqrt{53}+10$ units