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.

Formula

Formula: on a Number Line

If the endpoints of AB are A(x1) and B(x2),
then the midpoint of AB is
the mean of the endpoints:
M([x1 + x2]/2).

Formula: on a Coordinate Plane

If the endpoints of AB are A(x1, y1) and B(x2, y2),
then the midpoint of AB is
M([x1 + x2]/2, [y1 + y2]/2).

Example 1

Example 1

Solution

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.

Example 2

Example 2

Solution

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).

Example 3

Example 3

Solution

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.