Question

use the ordered pairs to form the vertices of a figure. then find the area of the figure. 2) (-3,2), (-2,2), (-2,3), (2,3), (2,-5), (-3,-5)

Explanation:

Step1: Identify the shape

By plotting the points (-3,2), (-2,2), (-2,3), (2,3), (2,-5), (-3,-5) on the coordinate - plane, we can see that the figure is a trapezoid.

Step2: Recall the area formula for a trapezoid

The formula for the area of a trapezoid is $A=\frac{1}{2}(b_1 + b_2)h$, where $b_1$ and $b_2$ are the lengths of the parallel sides and $h$ is the height between them.

Step3: Find the lengths of the parallel sides and the height

The length of the first parallel side $b_1$:
The points (-3,2) and (-2,2) give a horizontal line - segment. Using the distance formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ which is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Since $y_1 = y_2 = 2$, $b_1=\vert-2-(-3)\vert=1$.
The length of the second parallel side $b_2$:
The points (2,3) and (2,-5) give a vertical line - segment. Using the distance formula, since $x_1 = x_2 = 2$, $b_2=\vert3-(-5)\vert = 8$.
The height $h$:
The horizontal distance between the non - parallel sides. Consider the $x$ - coordinates of the non - parallel sides. The distance between $x=-2$ and $x = 2$ is $h=\vert2-(-2)\vert=4$.

Step4: Calculate the area

Substitute $b_1 = 1$, $b_2 = 8$, and $h = 4$ into the area formula:
$A=\frac{1}{2}(1 + 8)\times4=\frac{1}{2}\times9\times4=18$.

Answer:

18