Question

kite wxyz is graphed on a coordinate plane. what is the area of the kite? 7 square units 8 square units 14 square units 16 square units

Explanation:

Step1: Find the lengths of the diagonals

The formula for the area of a kite is \(A=\frac{1}{2}d_1d_2\), where \(d_1\) and \(d_2\) are the lengths of the diagonals.
From the graph, the length of diagonal \(WY\): The distance between \(W(-1,1)\) and \(Y(4,1)\) is \(d_{WY}=\vert4 - (- 1)\vert=5\) (using the distance formula for horizontal points \(d=\vert x_2 - x_1\vert\) since \(y_1 = y_2 = 1\)). The length of diagonal \(XZ\): The distance between \(X(2,4)\) and \(Z(2,-3)\) is \(d_{XZ}=\vert4-(-3)\vert = 7\) (using the distance formula for vertical points \(d=\vert y_2 - y_1\vert\) since \(x_1=x_2 = 2\)).

Step2: Calculate the area of the kite

Substitute \(d_1 = 7\) and \(d_2 = 4\) into the formula \(A=\frac{1}{2}d_1d_2\).
\(A=\frac{1}{2}\times7\times4\)
\(A = 14\)

Answer:

14 square units