Pre-Algebra Examples

$(0, y)$ , $(3, 0)$ , $(7, 4)$ , $(- 2, 1)$

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:

$(0, y)$ and $(3, 0)$ is $\sqrt{9 + y^{2}}$

$(0, y)$ and $(7, 4)$ is $\sqrt{65 - 8 y + y^{2}}$

$(0, y)$ and $(- 2, 1)$ is $\sqrt{5 - 2 y + y^{2}}$

$(3, 0)$ and $(7, 4)$ is $4 \sqrt{2}$

$(7, 4)$ and $(- 2, 1)$ is $3 \sqrt{10}$

$(3, 0)$ and $(- 2, 1)$ is $\sqrt{26}$

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