midpoint


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 (x1, y1) and (x2, y2) is given by

Example of Midpoint

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

Solved Example on Midpoint

is a line segment with end points A (- 2, - 4) and B (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 are A (- 2, - 4) and B (4, - 4).
Step 2: Let the mid point be C (x, y).
Step 3: The coordinates of C are (- 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