Question

a kite has vertices at (2,4),(5,4),(5,1), and (0, - 1). what is the approximate perimeter of the kite? round to the nearest tenth. 16.8 units 20.0 units 11.3 units 13.6 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 the points \((2,4)\) and \((5,4)\):
\(d_1=\sqrt{(5 - 2)^2+(4 - 4)^2}=\sqrt{3^2+0^2}=3\).
For the points \((5,4)\) and \((5,1)\):
\(d_2=\sqrt{(5 - 5)^2+(1 - 4)^2}=\sqrt{0^2+(- 3)^2}=3\).
For the points \((5,1)\) and \((0,-1)\):
\(d_3=\sqrt{(0 - 5)^2+(-1 - 1)^2}=\sqrt{(-5)^2+(-2)^2}=\sqrt{25 + 4}=\sqrt{29}\approx5.4\).
For the points \((0,-1)\) and \((2,4)\):
\(d_4=\sqrt{(2 - 0)^2+(4+1)^2}=\sqrt{2^2+5^2}=\sqrt{4 + 25}=\sqrt{29}\approx5.4\).

Step2: Calculate the perimeter

The perimeter \(P\) of the kite is \(P=d_1 + d_2+d_3 + d_4\).
\(P=3 + 3+5.4+5.4=16.8\).

Answer:

16.8 units