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 (x 1, y 1) and (x 2, y 2) is given by 
Examples 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
Video Examples: How To Find The Midpoint Using The Midpoint Formula
Solved Example on Midpoint
Ques: 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).
Quick Summary
- A line segment has only one midpoint.
- The midpoint divides the line segment into two equal parts.
🍎 Teacher Insights
Use visual aids and real-world examples to illustrate the concept of midpoint. Emphasize the importance of correctly identifying the coordinates of the endpoints before applying the formula.🎓 Prerequisites
- Basic Algebra
- Coordinate Plane
- Line Segment
Check Your Knowledge
Q1: Find the midpoint of the line segment with endpoints A(-2, -4) and B(4, -4).
Q2: If the midpoint of a line segment is (3, 2) and one endpoint is (1, 0), what is the other endpoint?
Frequently Asked Questions
Q: How do you find the midpoint if you only know one endpoint and the length of the segment?
A: You need to know either both endpoints or one endpoint and the midpoint. If you know one endpoint and the length, you cannot uniquely determine the midpoint.
Q: Is the midpoint always an integer?
A: No, the coordinates of the midpoint can be fractions or decimals, even if the endpoints have integer coordinates.