Question

What is the perimeter of this rectangle? a graph plot four points x subscript 1, y subscript 1 (bottom left), x subscript 1, y subscript 2 (top left), x subscript 2, y subscript 2 (top right) and x subscript 2, y subscript 1 (bottom right) completes a rectangle and the area is shaded. a. 2(x2 ? x1) 2(y2 ? y1) b. (x2 ? x1)(y2 ? y1) c. d. e. 4(y2 ? x1)(x2 ? y1)

Answer 1

The correct expression for the perimeter of the given rectangle is 2(x₂ - x₁) + 2(y₂ - y₁).

Step-by-step explanation:

In a rectangle, the perimeter is the sum of the lengths of all four sides. For the horizontal sides, the length is given by the difference between the x-coordinates of the corresponding points, which is (x₂ - x₁). Similarly, for the vertical sides, the length is given by the difference between the y-coordinates of the corresponding points, which is (y₂ - y₁). Therefore, the total perimeter is the sum of these lengths for all four sides.

Now, let's break down the expression: 2(x₂ - x₁) + 2(y₂ - y₁).

The first term, 2(x₂ - x₁), represents the sum of the lengths of the bottom and top sides of the rectangle. The factor of 2 is because there are two sides with lengths (x₂ - x₁).

The second term, 2(y₂ - y₁), represents the sum of the lengths of the left and right sides of the rectangle. Again, the factor of 2 is because there are two sides with lengths (y₂ - y₁).

Adding these two terms together gives the total perimeter of the rectangle. This expression is more simplified and straightforward than the other options, making it the correct choice for calculating the perimeter of the given rectangle.