Algebra Examples

$(\sqrt{18}, 2)$ , $(\sqrt{2}, - 2)$

Step 1

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 1.1

Factor $9$ out of $18$ .

$(\sqrt{9 (2)}, 2) - (\sqrt{2}, - 2)$

Step 1.2

Rewrite $9$ as $3^{2}$ .

$(\sqrt{3^{2} \cdot 2}, 2) - (\sqrt{2}, - 2)$

Step 2

Pull terms out from under the radical.

$(3 \sqrt{2}, 2) - (\sqrt{2}, - 2)$

Step 3

Use the midpoint formula to find the midpoint of the line segment.

$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Step 4

Substitute in the values for $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

$(\frac{3 \sqrt{2} + \sqrt{2}}{2}, \frac{2 - 2}{2})$

Step 5

Add $3 \sqrt{2}$ and $\sqrt{2}$ .

$(\frac{4 \sqrt{2}}{2}, \frac{2 - 2}{2})$

Step 6

Cancel the common factor of $4$ and $2$ .

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Step 6.1

Factor $2$ out of $4 \sqrt{2}$ .

$(\frac{2 (2 \sqrt{2})}{2}, \frac{2 - 2}{2})$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $2$ .

$(\frac{2 (2 \sqrt{2})}{2 (1)}, \frac{2 - 2}{2})$

Step 6.2.2

Cancel the common factor.

$(\frac{2 (2 \sqrt{2})}{2 \cdot 1}, \frac{2 - 2}{2})$

Step 6.2.3

Rewrite the expression.

$(\frac{2 \sqrt{2}}{1}, \frac{2 - 2}{2})$

Step 6.2.4

Divide $2 \sqrt{2}$ by $1$ .

$(2 \sqrt{2}, \frac{2 - 2}{2})$

Step 7

Cancel the common factor of $2 - 2$ and $2$ .

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Step 7.1

Factor $2$ out of $2$ .

$(2 \sqrt{2}, \frac{2 \cdot 1 - 2}{2})$

Step 7.2

Factor $2$ out of $- 2$ .

$(2 \sqrt{2}, \frac{2 \cdot 1 + 2 \cdot - 1}{2})$

Step 7.3

Factor $2$ out of $2 \cdot 1 + 2 \cdot - 1$ .

$(2 \sqrt{2}, \frac{2 \cdot (1 - 1)}{2})$

Step 7.4

Cancel the common factors.

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Step 7.4.1

Factor $2$ out of $2$ .

$(2 \sqrt{2}, \frac{2 \cdot (1 - 1)}{2 (1)})$

Step 7.4.2

Cancel the common factor.

$(2 \sqrt{2}, \frac{2 \cdot (1 - 1)}{2 \cdot 1})$

Step 7.4.3

Rewrite the expression.

$(2 \sqrt{2}, \frac{1 - 1}{1})$

Step 7.4.4

Divide $1 - 1$ by $1$ .

$(2 \sqrt{2}, 1 - 1)$

Step 8

Subtract $1$ from $1$ .

$(2 \sqrt{2}, 0)$

Step 9