Precalculus Examples

$(0, 0)$ , $(- 6, 6)$

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

$x_{1} = 2 (0) - (- 6)$

Step 5

Simplify the right side of $x_{1} = 2 (0) - (- 6)$ .

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $2$ by $0$ .

$x_{1} = 0 - (- 6)$

Step 5.1.2

Multiply $- 1$ by $- 6$ .

$x_{1} = 0 + 6$

Step 5.2

Add $0$ and $6$ .

$x_{1} = 6$

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

$y_{1} = 2 (0) - (6)$

Step 9

Simplify the right side of $y_{1} = 2 (0) - (6)$ .

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Step 9.1

Simplify each term.

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Step 9.1.1

Multiply $2$ by $0$ .

$y_{1} = 0 - (6)$

Step 9.1.2

Multiply $- 1$ by $6$ .

$y_{1} = 0 - 6$

Step 9.2

Subtract $6$ from $0$ .

$y_{1} = - 6$

Step 10

The start point is $(6, - 6)$ .

$(6, - 6)$

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