Algebra Examples

What is the midpoint of the line segment connecting the points $(- 2, 4)$ and $(2, 6)$ ?

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

$(\frac{- 2 + 2}{2}, \frac{4 + 6}{2})$

Step 3

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

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Step 3.1

Factor $2$ out of $- 2$ .

$(\frac{2 \cdot - 1 + 2}{2}, \frac{4 + 6}{2})$

Step 3.2

Factor $2$ out of $2$ .

$(\frac{2 \cdot - 1 + 2 \cdot 1}{2}, \frac{4 + 6}{2})$

Step 3.3

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

$(\frac{2 \cdot (- 1 + 1)}{2}, \frac{4 + 6}{2})$

Step 3.4

Cancel the common factors.

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Step 3.4.1

Factor $2$ out of $2$ .

$(\frac{2 \cdot (- 1 + 1)}{2 (1)}, \frac{4 + 6}{2})$

Step 3.4.2

Cancel the common factor.

$(\frac{2 \cdot (- 1 + 1)}{2 \cdot 1}, \frac{4 + 6}{2})$

Step 3.4.3

Rewrite the expression.

$(\frac{- 1 + 1}{1}, \frac{4 + 6}{2})$

Step 3.4.4

Divide $- 1 + 1$ by $1$ .

$(- 1 + 1, \frac{4 + 6}{2})$

Step 4

Add $- 1$ and $1$ .

$(0, \frac{4 + 6}{2})$

Step 5

Cancel the common factor of $4 + 6$ and $2$ .

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Step 5.1

Factor $2$ out of $4$ .

$(0, \frac{2 \cdot 2 + 6}{2})$

Step 5.2

Factor $2$ out of $6$ .

$(0, \frac{2 \cdot 2 + 2 \cdot 3}{2})$

Step 5.3

Factor $2$ out of $2 \cdot 2 + 2 \cdot 3$ .

$(0, \frac{2 \cdot (2 + 3)}{2})$

Step 5.4

Cancel the common factors.

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Step 5.4.1

Factor $2$ out of $2$ .

$(0, \frac{2 \cdot (2 + 3)}{2 (1)})$

Step 5.4.2

Cancel the common factor.

$(0, \frac{2 \cdot (2 + 3)}{2 \cdot 1})$

Step 5.4.3

Rewrite the expression.

$(0, \frac{2 + 3}{1})$

Step 5.4.4

Divide $2 + 3$ by $1$ .

$(0, 2 + 3)$

Step 6

Add $2$ and $3$ .

$(0, 5)$

Step 7