Algebra Examples

$(1, 2)$ ,

$(- 1, - 3)$

Step 1

The midpoint formula is

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

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

Step 2

Set the

$x_{M}$ equal to the

$x_{M}$ coordinate.

$x_{M} = \frac{x_{1} + x_{2}}{2}$

Step 3

Solve for

$x_{1}$ to get

$x_{1} = 2 x_{M} - x_{2}$ .

$x_{1} = 2 x_{M} - x_{2}$

Step 4

Substitute the values for

$x_{M}$ and

$x_{2}$ in

$x_{1} = 2 x_{M} - x_{2}$ .

$x_{1} = 2 (1) - (- 1)$

Step 5

Simplify the right side of

$x_{1} = 2 (1) - (- 1)$ .

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply

$2$ by

$1$ .

$x_{1} = 2 - (- 1)$

Step 5.1.2

Multiply

$- 1$ by

$- 1$ .

$x_{1} = 2 + 1$

Step 5.2

Add

$2$ and

$1$ .

$x_{1} = 3$

Step 6

Set the

$y_{M}$ equal to the

$y_{M}$ coordinate.

$y_{M} = \frac{y_{1} + y_{M}}{2}$

Step 7

Solve for

$y_{1}$ .

$y_{1} = 2 y_{M} - y_{2}$

Step 8

Substitute the values for

$y_{M}$ and

$y_{2}$ in

$y_{1} = 2 y_{M} - y_{2}$ .

$y_{1} = 2 (2) - (- 3)$

Step 9

Simplify the right side of

$y_{1} = 2 (2) - (- 3)$ .

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Step 9.1

Simplify each term.

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Step 9.1.1

Multiply

$2$ by

$2$ .

$y_{1} = 4 - (- 3)$

Step 9.1.2

Multiply

$- 1$ by

$- 3$ .

$y_{1} = 4 + 3$

Step 9.2

Add

$4$ and

$3$ .

$y_{1} = 7$

Step 10

The start point is

$(3, 7)$ .

$(3, 7)$

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