# Midpoint Formula

How to find the midpoint of a line segment by using the midpoint formula: 2 formulas (number line, coordinate plane), 3 example, and their solutions.

## Formulaon a Number Line

If the endpoints of AB are A(x_{1}) and B(x_{2}),

then the midpoint of AB is

the mean of the endpoints:

M([x_{1} + x_{2}]/2).

## ExampleMidpoint of A(-1), B(5)

Set the mipoint of AB M.

The endpoints of AB are

A(-1) and B(5).

Then the midpoint M is

[-1 + 5]/2.

-1 + 5 = 4

4/2 = 2

So 2 is the answer.

## Formulaon a Coordinate Plane

If the endpoints of AB are A(x_{1}, y_{1}) and B(x_{2}, y_{2}),

then the midpoint of AB is

M([x_{1} + x_{2}]/2, [y_{1} + y_{2}]/2).

## ExampleMidpoint of A(-3, 1), B(5, 4)

Set the mipoint of AB M.

The endpoints of AB are

A(-3, 1) and B(5, 4).

Then the midpoint M is

M([-3 + 5]/2, [1 + 4]/2).

-3 + 5 = 2

1 + 4 = 5

2/2 = 1

So M(1, 5/2).

## ExampleA(-4, 5), Midpoint: (0, 2), B = ?

Set the coordinates of point B

(p, q).

It says

point M is the midpoint of AB.

A(-4, 5)

B(p, q)

Then M([-4 + p]/2, [5 + q]/2).

M(0, 2)

So write = (0, 2).

So M([-4 + p]/2, [5 + q]/2) = (0, 2).

The x coordinates are the same.

So [-4 + p]/2 = 0.

Multiply 2 to both sides.

Move -4 to the right side.

Then p = 4.

The y coordinates are the same.

So [5 + q]/2 = 2.

Multiply 2 to both sides.

Move 5 to the right side.

Then q = -1.

B(p, q)

p = 4

q = -1

So B(4, -1).

So B(4, -1) is the answer.