Question

rectangle abcd is graphed in the coordinate plane. the following are the vertices of the rectangle: a(-2, 2), b(6, 2), c(6, 3), and d(-2, 3). what is the area of rectangle abcd? square units

Explanation:

Step1: Find the length of AB

Points A(-2, 2) and B(6, 2) have the same y - coordinate. The distance between them is calculated by the formula for the distance between two points with the same y - coordinate: \(d=\vert x_2 - x_1\vert\). So, the length of AB is \(\vert6 - (-2)\vert=\vert6 + 2\vert = 8\).

Step2: Find the length of BC

Points B(6, 2) and C(6, 3) have the same x - coordinate. The distance between them is calculated by the formula for the distance between two points with the same x - coordinate: \(d=\vert y_2 - y_1\vert\). So, the length of BC is \(\vert3 - 2\vert=1\).

Step3: Calculate the area of the rectangle

The area of a rectangle is given by the formula \(A = \text{length}\times\text{width}\). Here, length = AB = 8 and width = BC = 1. So, the area \(A=8\times1 = 8\).

Answer:

8