Find the Midpoint ( square root of 18,5) , ( square root of 2,-5)

$(\sqrt{18}, 5)$ , $(\sqrt{2}, - 5)$

Step 1

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

Factor $9$ out of $18$ .

$(\sqrt{9 (2)}, 5) - (\sqrt{2}, - 5)$

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

$(\sqrt{3^{2} \cdot 2}, 5) - (\sqrt{2}, - 5)$

Step 2

Pull terms out from under the radical.

$(3 \sqrt{2}, 5) - (\sqrt{2}, - 5)$

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 $(x_{2}, y_{2})$ .

$(\frac{3 \sqrt{2} + \sqrt{2}}{2}, \frac{5 - 5}{2})$

Step 5

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

$(\frac{4 \sqrt{2}}{2}, \frac{5 - 5}{2})$

Step 6

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

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

$(\frac{2 (2 \sqrt{2})}{2}, \frac{5 - 5}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(\frac{2 (2 \sqrt{2})}{2 (1)}, \frac{5 - 5}{2})$

Cancel the common factor.

$(\frac{2 (2 \sqrt{2})}{2 \cdot 1}, \frac{5 - 5}{2})$

Rewrite the expression.

$(\frac{2 \sqrt{2}}{1}, \frac{5 - 5}{2})$

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

$(2 \sqrt{2}, \frac{5 - 5}{2})$

Step 7

Subtract $5$ from $5$ .

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

Step 8

Divide $0$ by $2$ .

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

Step 9