Algebra Examples

$(9 \sqrt{5}, - \sqrt{10})$ , $(- \sqrt{5}, 0)$

Step 1

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 2

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

$(\frac{9 \sqrt{5} - \sqrt{5}}{2}, \frac{- \sqrt{10} + 0}{2})$

Step 3

Subtract $\sqrt{5}$ from $9 \sqrt{5}$ .

$(\frac{8 \sqrt{5}}{2}, \frac{- \sqrt{10} + 0}{2})$

Step 4

Cancel the common factor of $8$ and $2$ .

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Step 4.1

Factor $2$ out of $8 \sqrt{5}$ .

$(\frac{2 (4 \sqrt{5})}{2}, \frac{- \sqrt{10} + 0}{2})$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $2$ .

$(\frac{2 (4 \sqrt{5})}{2 (1)}, \frac{- \sqrt{10} + 0}{2})$

Step 4.2.2

Cancel the common factor.

$(\frac{2 (4 \sqrt{5})}{2 \cdot 1}, \frac{- \sqrt{10} + 0}{2})$

Step 4.2.3

Rewrite the expression.

$(\frac{4 \sqrt{5}}{1}, \frac{- \sqrt{10} + 0}{2})$

Step 4.2.4

Divide $4 \sqrt{5}$ by $1$ .

$(4 \sqrt{5}, \frac{- \sqrt{10} + 0}{2})$

Step 5

Add $- \sqrt{10}$ and $0$ .

$(4 \sqrt{5}, \frac{- \sqrt{10}}{2})$

Step 6

Move the negative in front of the fraction.

$(4 \sqrt{5}, - \frac{\sqrt{10}}{2})$

Step 7