Learn how to find an endpoint using the midpoint of a segment with a couple of good examples.

**Example #1:**

The midpoint of a segment is M(2, 3). One endpoint is A(-2, -1). Find the other coordinates of the other endpoint B.

Use the midpoint formula M[(x_{1} + x_{2})/2, (y_{1} + y_{2})/2] and let the coordinates of B be (x_{2}, y_{2})

Notice that (x_{1} + x_{2})/2 is the x-coordinate of the midpoint. So (x_{1} + x_{2})/2 = 2

Notice that (y_{1} + y_{2})/2 is the y-coordinate of the midpoint. So (y_{1} + y_{2})/2 = 3

Let x_{1} = -2 and y_{1} = -1 and solve the two equations below:

**(-2 + x _{2})/2 = 2** and

Solve (-1 + y_{2})/2 = 3

Multiply both sides of (-1 + y_{2})/2 = 3 by 2

2(-1 + y_{2})/2 = 3(2)

Simplify

-1 + y_{2} = 6

Add 1 to both sides of the equation

-1 + 1 + y_{2} = 6 + 1

Simplify

**y _{2} = 7**

Solve (-2 + x_{2})/2 = 2

Multiply both sides of (-2 + x_{2})/2 = 2 by 2

2(-2 + x_{2})/2 = 2(2)

Simplify

-2 + x_{2} = 4

Add 2 to both sides of the equation

-2 + 2 + x_{2} = 4 + 2

Simplify

**x _{2} = 6**

The coordinates other endpoint B are (6, 7)

**Example #2:**

The midpoint of a segment is M(-1, 0). One endpoint is A(5, 6). Find the other coordinates of the other endpoint B.

Use the midpoint formula M[(x_{1} + x_{2})/2, (y_{1} + y_{2})/2] and let the coordinates of B be (x_{2}, y_{2})

Let x_{1} = 5 and y_{1} = 6 and solve the two equations below:

**(5 + x _{2})/2 = -1** and

Solve (6 + y_{2})/2 = 0

Multiply both sides of (6 + y_{2})/2 = 0 by 2

2(6 + y_{2})/2 = 0(2)

Simplify

6 + y_{2} = 0

Subtract 6 from both sides of the equation

6 - 6 + y_{2} = 0 - 6

Simplify

**y _{2} = -6**

Solve (5 + x_{2})/2 = -1

Multiply both sides of (5 + x_{2})/2 = -1 by 2

2(5 + x_{2})/2 = -1(2)

Simplify

5 + x_{2} = -2

Subtract 5 from both sides of the equation

5 - 5 + x_{2} = -2 - 5

Simplify

**x _{2} = -7**

The coordinates other endpoint B are (-7, -6)