Find the End Point Given Start (6,4) and Mid (2,1) (6,4) , (2,1)

$(6, 4)$ , $(2, 1)$

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

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

Step 5

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

Simplify each term.

Multiply $2$ by $2$ .

$x_{2} = 4 - (6)$

Multiply $- 1$ by $6$ .

$x_{2} = 4 - 6$

Subtract $6$ from $4$ .

$x_{2} = - 2$

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

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

Step 9

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

Simplify each term.

Multiply $2$ by $1$ .

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

Multiply $- 1$ by $4$ .

$y_{2} = 2 - 4$

Subtract $4$ from $2$ .

$y_{2} = - 2$

Step 10

The end point is $(- 2, - 2)$ .

$(- 2, - 2)$