Question

what is the perimeter of this rectangle? (x1, y2) (x2, y2) (x1, y1) (x2, y1) a. 2(x2 - x1)+2(y2 - y1) b. (x2 - x1)(y2 - y1) c. \sqrt{2(y2 - y1)(x2 - x1)} d. 4\sqrt{(y2 - y1)^2(x2 - x1)^2} e. 4(y2 - x1)(x2 - y1)

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2l+2w$, where $l$ is the length and $w$ is the width.

Step2: Find length and width

The length of the rectangle is the horizontal - distance between $(x_1,y_1)$ and $(x_2,y_1)$ which is $|x_2 - x_1|$. The width of the rectangle is the vertical - distance between $(x_1,y_1)$ and $(x_1,y_2)$ which is $|y_2 - y_1|$.

Step3: Calculate perimeter

Substitute length and width into the perimeter formula: $P=2|x_2 - x_1|+2|y_2 - y_1|$. Since $x_2>x_1$ and $y_2 > y_1$ (assuming the normal orientation of a rectangle in a coordinate - plane), we have $P = 2(x_2 - x_1)+2(y_2 - y_1)$.

Answer:

A. $2(x_2 - x_1)+2(y_2 - y_1)$