Pre-Algebra Examples

(0, y)

$(0, y)$ ,

(3, 0)

$(3, 0)$ ,

(7, 4)

$(7, 4)$ ,

(- 2, 1)

$(- 2, 1)$

Step 1

Every rectangle has three different pairs that have the same length. One pair contains the length

l

$l$ , another pair contains the width

w

$w$ , and the last pair contains the diagonal

d

$d$ .

The distance between:

(0, y)

$(0, y)$ and

(3, 0)

$(3, 0)$ is

\sqrt{9 + y^{2}}

$\sqrt{9 + y^{2}}$

(0, y)

$(0, y)$ and

(7, 4)

$(7, 4)$ is

\sqrt{65 - 8 y + y^{2}}

$\sqrt{65 - 8 y + y^{2}}$

(0, y)

$(0, y)$ and

(- 2, 1)

$(- 2, 1)$ is

\sqrt{5 - 2 y + y^{2}}

$\sqrt{5 - 2 y + y^{2}}$

(3, 0)

$(3, 0)$ and

(7, 4)

$(7, 4)$ is

4 \sqrt{2}

$4 \sqrt{2}$

(7, 4)

$(7, 4)$ and

(- 2, 1)

$(- 2, 1)$ is

3 \sqrt{10}

$3 \sqrt{10}$

(3, 0)

$(3, 0)$ and

(- 2, 1)

$(- 2, 1)$ is

\sqrt{26}

$\sqrt{26}$

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

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

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

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