Pre-Algebra Examples

$(- 4, - 7)$ , $(1, 3)$ , $(2, 6)$ , $(4, 10)$

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:

$(- 4, - 7)$ and $(1, 3)$ is $5 \sqrt{5}$

$(- 4, - 7)$ and $(2, 6)$ is $\sqrt{205}$

$(- 4, - 7)$ and $(4, 10)$ is $\sqrt{353}$

$(1, 3)$ and $(2, 6)$ is $\sqrt{10}$

$(2, 6)$ and $(4, 10)$ is $2 \sqrt{5}$

$(1, 3)$ and $(4, 10)$ is $\sqrt{58}$

Step 2

The distances between the points show that there are no three different pairs that contain the length, width, and diagonal and have the same length, so the shape is not a rectangle.

Not a rectangle

Step 3