Question

what is the area of the rhombus?

Explanation:

Step1: Recall area formula for rhombus

The area formula of a rhombus is $A=\frac{1}{2}d_1d_2$, where $d_1$ and $d_2$ are the lengths of the diagonals.

Step2: Find length of first diagonal

The two points of one diagonal are $(- 2,-1)$ and $(8,-1)$. Since the $y$ - coordinates are the same, the length of this diagonal $d_1$ is given by the distance formula for two - points with the same $y$ - coordinate: $d_1=\vert x_2 - x_1\vert$. Here, $x_1=-2$ and $x_2 = 8$, so $d_1=\vert8-(-2)\vert=10$.

Step3: Find length of second diagonal

The two points of the other diagonal are $(3,7)$ and $(3,-9)$. Since the $x$ - coordinates are the same, the length of this diagonal $d_2$ is given by the distance formula for two - points with the same $x$ - coordinate: $d_2=\vert y_2 - y_1\vert$. Here, $y_1 = 7$ and $y_2=-9$, so $d_2=\vert-9 - 7\vert = 16$.

Step4: Calculate the area

Substitute $d_1 = 10$ and $d_2=16$ into the area formula $A=\frac{1}{2}d_1d_2$. We get $A=\frac{1}{2}\times10\times16=80$.

Answer:

80