Precalculus Examples

(0, 9)

$(0, 9)$ ,

(8, 6)

$(8, 6)$

Step 1

The midpoint formula is

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

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

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}

$x_{M}$ equal to the

x_{M}

$x_{M}$ coordinate.

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

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

Step 3

Solve for

x_{1}

$x_{1}$ to get

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

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

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

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

Step 4

Substitute the values for

x_{M}

$x_{M}$ and

x_{2}

$x_{2}$ in

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

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

x_{1} = 2 (0) - (8)

$x_{1} = 2 (0) - (8)$

Step 5

Simplify the right side of

x_{1} = 2 (0) - (8)

$x_{1} = 2 (0) - (8)$ .

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply

2

$2$ by

0

$0$ .

x_{1} = 0 - (8)

$x_{1} = 0 - (8)$

Step 5.1.2

Multiply

- 1

$- 1$ by

8

$8$ .

x_{1} = 0 - 8

$x_{1} = 0 - 8$

x_{1} = 0 - 8

$x_{1} = 0 - 8$

Step 5.2

Subtract

8

$8$ from

0

$0$ .

x_{1} = - 8

$x_{1} = - 8$

x_{1} = - 8

$x_{1} = - 8$

Step 6

Set the

y_{M}

$y_{M}$ equal to the

y_{M}

$y_{M}$ coordinate.

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

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

Step 7

Solve for

y_{1}

$y_{1}$ .

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

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

Step 8

Substitute the values for

y_{M}

$y_{M}$ and

y_{2}

$y_{2}$ in

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

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

y_{1} = 2 (9) - (6)

$y_{1} = 2 (9) - (6)$

Step 9

Simplify the right side of

y_{1} = 2 (9) - (6)

$y_{1} = 2 (9) - (6)$ .

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Step 9.1

Simplify each term.

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Step 9.1.1

Multiply

2

$2$ by

9

$9$ .

y_{1} = 18 - (6)

$y_{1} = 18 - (6)$

Step 9.1.2

Multiply

- 1

$- 1$ by

6

$6$ .

y_{1} = 18 - 6

$y_{1} = 18 - 6$

y_{1} = 18 - 6

$y_{1} = 18 - 6$

Step 9.2

Subtract

6

$6$ from

18

$18$ .

y_{1} = 12

$y_{1} = 12$

y_{1} = 12

$y_{1} = 12$

Step 10

The start point is

(- 8, 12)

$(- 8, 12)$ .

(- 8, 12)

$(- 8, 12)$

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