Question

what is the perimeter of kite wxyz? 2√53 + 2 units 2√53 + 5 units 2√53 + 10 units 2√53 + 14 units w(-3,3) x(2,3) z(-3,-2) y(4,-4)

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 WX

For points $W(-3,3)$ and $X(2,3)$, $x_1=-3,y_1 = 3,x_2=2,y_2 = 3$. Then $d_{WX}=\sqrt{(2+3)^2+(3 - 3)^2}=\sqrt{25+0}=5$.

Step3: Calculate length of WZ

For points $W(-3,3)$ and $Z(-3,-2)$, $x_1=-3,y_1 = 3,x_2=-3,y_2=-2$. Then $d_{WZ}=\sqrt{(-3 + 3)^2+(-2 - 3)^2}=\sqrt{0 + 25}=5$.

Step4: Calculate length of XY

For points $X(2,3)$ and $Y(4,-4)$, $d_{XY}=\sqrt{(4 - 2)^2+(-4 - 3)^2}=\sqrt{4 + 49}=\sqrt{53}$.

Step5: Calculate length of YZ

For points $Y(4,-4)$ and $Z(-3,-2)$, $d_{YZ}=\sqrt{(-3 - 4)^2+(-2 + 4)^2}=\sqrt{49+4}=\sqrt{53}$.

Step6: Calculate perimeter

The perimeter $P$ of the kite is $P=d_{WX}+d_{WZ}+d_{XY}+d_{YZ}=5 + 5+\sqrt{53}+\sqrt{53}=2\sqrt{53}+10$.

Answer:

$2\sqrt{53}+10$ units