Question

Find the perimeter or circumference and area of the square with vertices A(-2, 7), B(4, 4), C(2, 0), and D(-4, 3) if each unit on the graph measures 1 centimeter.

Answer 1

We first apply the distance formula to find the length of one side of the square. The perimeter of the square can be found by multiplying the side length by 4, while the area corresponds to the square of the side length.

Step-by-step explanation:

First, you need to find the length of one side of the square to calculate its perimeter and area. Using the distance formula, we can find the length of side AB. The distance formula is as follows: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). So, let's find the distance between points A and B. A(-2,7), B(4,4), therefore distance AB = sqrt((4 --2)^2 + (4 - 7)^2) = sqrt((6)^2 + (-3)^2) = sqrt((36 + 9) = sqrt(45). The perimeter of the square is four times the side length, hence P = 4 * sqrt(45) cm.

Next, to find the area, we square the length of the side of the square. Hence, A = (sqrt(45))^2 = 45 cm^2. Therefore, the perimeter of the square is 4 * sqrt(45) cm and the area is 45 cm^2.

Learn more about Square Perimeter and Area