Question

what is the area of the rhombus?

Explanation:

Step1: Find the lengths of the diagonals

The diagonals of a rhombus are perpendicular bisectors of each other. Let's find the lengths of the diagonals using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
The first diagonal connects $(-2,-1)$ and $(8,-1)$. Since the $y$-coordinates are the same, the length $d_1$ of this diagonal is $|8 - (-2)|=10$.
The second diagonal connects $(3,7)$ and $(3,-9)$. Since the $x$-coordinates are the same, the length $d_2$ of this diagonal is $|7-(-9)| = 16$.

Step2: Use the area formula for a rhombus

The area formula of a rhombus is $A=\frac{1}{2}d_1d_2$. Substitute $d_1 = 10$ and $d_2=16$ into the formula. So $A=\frac{1}{2}\times10\times16$.
$A = 80$.

Answer:

80