Find the Midpoint (2b,2c) , (2a,0)

$(2 b, 2 c)$ , $(2 a, 0)$

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

$(\frac{2 b + 2 a}{2}, \frac{2 c + 0}{2})$

Step 3

Cancel the common factor of $2 b + 2 a$ and $2$ .

Factor $2$ out of $2 b$ .

$(\frac{2 (b) + 2 a}{2}, \frac{2 c + 0}{2})$

Factor $2$ out of $2 a$ .

$(\frac{2 (b) + 2 (a)}{2}, \frac{2 c + 0}{2})$

Factor $2$ out of $2 (b) + 2 (a)$ .

$(\frac{2 (b + a)}{2}, \frac{2 c + 0}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(\frac{2 (b + a)}{2 (1)}, \frac{2 c + 0}{2})$

Cancel the common factor.

$(\frac{2 (b + a)}{2 \cdot 1}, \frac{2 c + 0}{2})$

Rewrite the expression.

$(\frac{b + a}{1}, \frac{2 c + 0}{2})$

Divide $b + a$ by $1$ .

$(b + a, \frac{2 c + 0}{2})$

Step 4

Cancel the common factor of $2 c + 0$ and $2$ .

Factor $2$ out of $2 c$ .

$(b + a, \frac{2 (c) + 0}{2})$

Factor $2$ out of $0$ .

$(b + a, \frac{2 (c) + 2 \cdot 0}{2})$

Factor $2$ out of $2 (c) + 2 (0)$ .

$(b + a, \frac{2 (c + 0)}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(b + a, \frac{2 (c + 0)}{2 (1)})$

Cancel the common factor.

$(b + a, \frac{2 (c + 0)}{2 \cdot 1})$

Rewrite the expression.

$(b + a, \frac{c + 0}{1})$

Divide $c + 0$ by $1$ .

$(b + a, c + 0)$

Step 5

Add $c$ and $0$ .

$(b + a, c)$