Question

which expression can be used to find the area of the rectangle shown on the coordinate plane? 7×7 6×7 8×7 8×8

Explanation:

Step1: Find the length of the rectangle

The length of the rectangle is the distance between \(x = 3\) and \(x = 4\) along the \(x -\)axis. Using the formula for the distance between two points \(d=\vert x_2 - x_1\vert\), if \(x_1 = 3\) and \(x_2=4\), then the length \(l=\vert4 - (- 3)\vert=7\) (since we count the number of units between the two \(x -\)coordinates of the vertical sides of the rectangle).

Step2: Find the width of the rectangle

The width of the rectangle is the distance between \(y=-5\) and \(y = 3\) along the \(y -\)axis. Using the formula for the distance between two points \(d=\vert y_2 - y_1\vert\), if \(y_1=-5\) and \(y_2 = 3\), then the width \(w=\vert3-(-5)\vert = 8\) (since we count the number of units between the two \(y -\)coordinates of the horizontal sides of the rectangle).

Step3: Calculate the area of the rectangle

The area of a rectangle is given by the formula \(A = l\times w\). Substituting \(l = 7\) and \(w = 8\) into the formula, we get \(A=8\times7\).

Answer:

\(8\times7\)