Find the End Point Given Start (2,5) and Mid (3,8) (2,5) , (3,8)

$(2, 5)$ , $(3, 8)$

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

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

Step 5

Simplify the right side of $x_{2} = 2 \cdot (3) - (2)$ .

Simplify each term.

Multiply $2$ by $3$ .

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

Multiply $- 1$ by $2$ .

$x_{2} = 6 - 2$

Subtract $2$ from $6$ .

$x_{2} = 4$

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

$y_{2} = 2 \cdot (8) - (5)$

Step 9

Simplify the right side of $y_{2} = 2 \cdot (8) - (5)$ .

Simplify each term.

Multiply $2$ by $8$ .

$y_{2} = 16 - (5)$

Multiply $- 1$ by $5$ .

$y_{2} = 16 - 5$

Subtract $5$ from $16$ .

$y_{2} = 11$

Step 10

The end point is $(4, 11)$ .

$(4, 11)$