Question

click or touch the the graph to plot points.
a rectangular plot of land has vertices located at (2,8),(2,2),(-4,2), and (-4,8).
melissa says the area is 36 square units. what do you think about melissas solution?
melissa is incorrect
because she did not
multiply dimensions.
melissa is incorrect
because she did not
add correctly.
melissa is correct.
melissa is incorrect
because she did not
use absolute value.

Explanation:

Step1: Calculate the length of the rectangle

The length of the rectangle can be found by calculating the distance between \((2,8)\) and \((-4,8)\) (since they have the same \(y -\)coordinate). Using the formula for the distance between two points \(d=\vert x_2 - x_1\vert\) (for points \((x_1,y_1)\) and \((x_2,y_2)\) with \(y_1 = y_2\)), we have \(d=\vert-4 - 2\vert=\vert-6\vert = 6\) units.

Step2: Calculate the width of the rectangle

The width of the rectangle can be found by calculating the distance between \((2,8)\) and \((2,2)\) (since they have the same \(x -\)coordinate). Using the formula \(d=\vert y_2 - y_1\vert\) (for points \((x_1,y_1)\) and \((x_2,y_2)\) with \(x_1 = x_2\)), we have \(d=\vert2 - 8\vert=\vert-6\vert=6\) units.

Step3: Calculate the area of the rectangle

The area of a rectangle is \(A=\text{length}\times\text{width}\). Substituting the values we found (\(\text{length}=6\) and \(\text{width}=6\)), we get \(A = 6\times6=36\) square units.

Answer:

Melissa is correct.