Algebra Examples

$(1, 4)$ , $(7, - 4)$

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

$x_{1} = 2 (1) - (7)$

Step 5

Simplify the right side of $x_{1} = 2 (1) - (7)$ .

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $2$ by $1$ .

$x_{1} = 2 - (7)$

Step 5.1.2

Multiply $- 1$ by $7$ .

$x_{1} = 2 - 7$

Step 5.2

Subtract $7$ from $2$ .

$x_{1} = - 5$

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

$y_{1} = 2 (4) - (- 4)$

Step 9

Simplify the right side of $y_{1} = 2 (4) - (- 4)$ .

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Step 9.1

Simplify each term.

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Step 9.1.1

Multiply $2$ by $4$ .

$y_{1} = 8 - (- 4)$

Step 9.1.2

Multiply $- 1$ by $- 4$ .

$y_{1} = 8 + 4$

Step 9.2

Add $8$ and $4$ .

$y_{1} = 12$

Step 10

The start point is $(- 5, 12)$ .

$(- 5, 12)$

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