Precalculus Examples

$(1, 1)$ , $(- 1, - 3.4)$

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 $x_{2}$ .

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

Step 4

Substitute the values for $x_{M}$ and $x_{1}$ in $x_{2} = 2 (x_{M}) - (x_{1})$ .

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

Step 5

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

Tap for more steps...

Step 5.1

Simplify each term.

Tap for more steps...

Step 5.1.1

Multiply $2$ by $- 1$ .

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

Step 5.1.2

Multiply $- 1$ by $1$ .

$x_{2} = - 2 - 1$

Step 5.2

Subtract $1$ from $- 2$ .

$x_{2} = - 3$

Step 6

Set the $y_{M}$ equal to the $y_{M}$ coordinate.

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

Step 7

Solve for $y_{2}$ .

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

Step 8

Substitute the values for $y_{M}$ and $y_{1}$ in $y_{2} = 2 (y_{M}) - (y_{1})$ .

$y_{2} = 2 \cdot (- 3.4) - (1)$

Step 9

Simplify the right side of $y_{2} = 2 \cdot (- 3.4) - (1)$ .

Tap for more steps...

Step 9.1

Simplify each term.

Tap for more steps...

Step 9.1.1

Multiply $2$ by $- 3.4$ .

$y_{2} = - 6.8 - (1)$

Step 9.1.2

Multiply $- 1$ by $1$ .

$y_{2} = - 6.8 - 1$

Step 9.2

Subtract $1$ from $- 6.8$ .

$y_{2} = - 7.8$

Step 10

The end point is $(- 3, - 7.8)$ .

$(- 3, - 7.8)$