# How do you find the coordinates of the other endpoint of a segment with the given midpoint (-3, 7) and one endpoint of a segment (5,-1)?

Apr 28, 2017

Use the midpoint formula but solve for one of the endpoints.

#### Explanation:

The Midpoint formula is:

x_"midpoint" = (x_"endpoint" + x_"startpoint")/2

and

y_"midpoint" = (y_"endpoint" + y_"startpoint")/2

Substitute -3 for ${x}_{\text{midpoint}}$ and 7 for ${y}_{\text{midpoint}}$

$- 3 = \frac{{x}_{\text{endpoint" + x_"startpoint}}}{2}$

and

$7 = \frac{{y}_{\text{endpoint" + y_"startpoint}}}{2}$

Substitute 5 for ${x}_{\text{startpoint}}$ and -1 for y_"startpoint":

$- 3 = \frac{{x}_{\text{endpoint}} + 5}{2}$

and

$7 = \frac{{y}_{\text{endpoint}} - 1}{2}$

We can solve the two equations for the endpoint:

$- 6 = {x}_{\text{endpoint}} + 5$

and

$14 = {y}_{\text{endpoint}} - 1$

${x}_{\text{endpoint}} = - 11$

and

${y}_{\text{endpoint}} = 15$

The endpoint is $\left(- 11 , 15\right)$