Precalculus Examples

(1, - 2)

$(1, - 2)$ ,

(3, 6)

$(3, 6)$

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_{2}

$x_{2}$ .

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

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

Step 4

Substitute the values for

x_{M}

$x_{M}$ and

x_{1}

$x_{1}$ in

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

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

x_{2} = 2 \cdot (3) - (1)

$x_{2} = 2 \cdot (3) - (1)$

Step 5

Simplify the right side of

x_{2} = 2 \cdot (3) - (1)

$x_{2} = 2 \cdot (3) - (1)$ .

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply

2

$2$ by

3

$3$ .

x_{2} = 6 - (1)

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

Step 5.1.2

Multiply

- 1

$- 1$ by

1

$1$ .

x_{2} = 6 - 1

$x_{2} = 6 - 1$

x_{2} = 6 - 1

$x_{2} = 6 - 1$

Step 5.2

Subtract

1

$1$ from

6

$6$ .

x_{2} = 5

$x_{2} = 5$

x_{2} = 5

$x_{2} = 5$

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_{2}

$y_{2}$ .

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

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

Step 8

Substitute the values for

y_{M}

$y_{M}$ and

y_{1}

$y_{1}$ in

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

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

y_{2} = 2 \cdot (6) - (- 2)

$y_{2} = 2 \cdot (6) - (- 2)$

Step 9

Simplify the right side of

y_{2} = 2 \cdot (6) - (- 2)

$y_{2} = 2 \cdot (6) - (- 2)$ .

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Step 9.1

Simplify each term.

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Step 9.1.1

Multiply

2

$2$ by

6

$6$ .

y_{2} = 12 - (- 2)

$y_{2} = 12 - (- 2)$

Step 9.1.2

Multiply

- 1

$- 1$ by

- 2

$- 2$ .

y_{2} = 12 + 2

$y_{2} = 12 + 2$

y_{2} = 12 + 2

$y_{2} = 12 + 2$

Step 9.2

Add

12

$12$ and

2

$2$ .

y_{2} = 14

$y_{2} = 14$

y_{2} = 14

$y_{2} = 14$

Step 10

The end point is

(5, 14)

$(5, 14)$ .

(5, 14)

$(5, 14)$

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