**Definition of Midpoint**

- Midpoint of a line segment is the point that is halfway between the endpoints of the line segment.

**More about Midpoint**

- A line segment has only one midpoint.
- If AB is a line segment and P is the midpoint, then AP = BP = .
- In two-dimensional coordinate plane, the midpoint of a line with coordinates of its endpoints as (
*x*_{1},*y*_{1}) and (*x*_{2},*y*_{2}) is given by

**Example of Midpoint**

- In the above figure, length of is 15 cm and distance of
*C*from both the endpoints*A*and*B*is 7.5 cm. So,*C*is the midpoint of .

**Solved Example on Midpoint**

is a line segment with end points

A(- 2, - 4) andB(4, - 4). Find the coordinates of the midpoint of .

Choices:

A. (1, - 4)

B. (- 1, 4)

C. (1, 4)

D. (- 1, - 4)

Correct Answer: A

Solution:

Step 1:The end points areA(- 2, - 4) andB(4, - 4).

Step 2:Let the mid point beC(x,y).

Step 3:The coordinates ofCare (- 2 + 42, - 4 - 42). [Use mid-point formula.]

Step 4:So, the coordinates of the midpoint are (1, - 4).

**Related Terms for Midpoint**

- Equal
- Half
- Line Segment
- Point