Algebra Examples

$(3, 2)$ , $(- 3, - 2)$ , $(- 3, 2)$ , $(3, - 2)$

Step 1

Every rectangle has three different pairs that have the same length. One pair contains the length $l$ , another pair contains the width $w$ , and the last pair contains the diagonal $d$ .

The distance between:

$(3, 2)$ and $(- 3, - 2)$ is $2 \sqrt{13}$

$(3, 2)$ and $(- 3, 2)$ is $6$

$(3, 2)$ and $(3, - 2)$ is $4$

$(- 3, - 2)$ and $(- 3, 2)$ is $4$

$(- 3, 2)$ and $(3, - 2)$ is $2 \sqrt{13}$

$(- 3, - 2)$ and $(3, - 2)$ is $6$

Step 2

The distances between the points show that there are three different pairs that have the same length. One pair contains the length, another pair contains the width, and the last pair contains the diagonal. The diagonal is the longest distance and the width is the shortest distance, which means $l = 6$ and $w = 4$ .

$l = 6$

$w = 4$

Step 3

The area of a rectangle is the product of the length and width, $A = l \cdot w$ .

$A = l \cdot w$

Step 4

Multiply $6$ by $4$ .

$A = 24$

Step 5