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: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(W(-3,3)\) and \(Z(-3,-2)\):
\(WZ=\sqrt{(-3-(-3))^2+(-2 - 3)^2}=\sqrt{0+(-5)^2}=5\)
For \(X(2,3)\) and \(Y(4,-4)\):
\(XY=\sqrt{(4 - 2)^2+(-4 - 3)^2}=\sqrt{4 + 49}=\sqrt{53}\)
For \(W(-3,3)\) and \(X(2,3)\):
\(WX=\sqrt{(2-(-3))^2+(3 - 3)^2}=\sqrt{25+0}=5\)
For \(Z(-3,-2)\) and \(Y(4,-4)\):
\(ZY=\sqrt{(4-(-3))^2+(-4-(-2))^2}=\sqrt{49 + 4}=\sqrt{53}\)

Step2: Calculate the perimeter

The perimeter \(P\) of a kite is \(P = 2a+2b\) (where \(a\) and \(b\) are the lengths of adjacent sides). Here \(a=\sqrt{53}\), \(b = 5\)
\(P=2\sqrt{53}+2\times5=2\sqrt{53}+10\)

Answer:

\(2\sqrt{53}+10\) units (the third option)