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: Identify the diagonals of the kite

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 coordinate plane, we first find the lengths of the two diagonals.

Looking at the coordinates:

• For the vertical diagonal (let's say $d_1$), the top vertex X is at (3, 4) and the bottom vertex Z is at (3, -3). The length of this diagonal is the difference in the y - coordinates: $|4 - (-3)|=|4 + 3| = 7$.
• For the horizontal diagonal (let's say $d_2$), the left vertex W is at (1, 1) and the right vertex Y is at (5, 1). The length of this diagonal is the difference in the x - coordinates: $|5 - 1|=4$.

Step2: Apply the area formula for a kite

Using the formula $A=\frac{1}{2}d_1d_2$, substitute $d_1 = 7$ and $d_2 = 4$.
$A=\frac{1}{2}\times7\times4$
First, calculate $7\times4 = 28$, then $\frac{1}{2}\times28=14$.

Answer:

14 square units