Question

pre - algebra ic sem 2 fall 2025
finding area on a coordinate plane
solving a real - world problem
marina is drawing a plan for a new garden. the rectangle plotted in the coordinate plane represents the garden, measured in feet. how much soil will she need to cover the garden?
20 ft²
12 ft²
10 ft²
24 ft²

Explanation:

Step1: Calculate the length of the rectangle

The length of the rectangle can be found by calculating the distance between two points on the same horizontal line. Using the formula for the distance between two points \(x_1\) and \(x_2\) on the x - axis (\(d=\vert x_2 - x_1\vert\)).
For the points \((- 2,1)\) and \((4,1)\), \(x_1=-2\), \(x_2 = 4\). Then \(l=\vert4-(-2)\vert=\vert4 + 2\vert=6\)

Step2: Calculate the width of the rectangle

The width of the rectangle can be found by calculating the distance between two points on the same vertical line. Using the formula for the distance between two points \(y_1\) and \(y_2\) on the y - axis (\(d=\vert y_2 - y_1\vert\)).
For the points \((-2,1)\) and \((-2,-3)\), \(y_1 = 1\), \(y_2=-3\). Then \(w=\vert-3 - 1\vert=\vert-4\vert=4\)

Step3: Calculate the area of the rectangle

The area of a rectangle is given by the formula \(A=l\times w\).
Substitute \(l = 6\) and \(w = 4\) into the formula: \(A=6\times4=24\)

Answer:

\(24\mathrm{ft}^2\)