How to Find the Midpoint

 

How to Find the Midpoint When Two Points Are Given

Definition:
The midpoint of a line segment is the point that is exactly in the middle of the two endpoints. It’s like the "average" of the two points.

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Formula to Find the Midpoint:

If you have two points on a graph:

• Point A: $(x_1,y_1)$

• Point B: $(x_2,y_2)$

The midpoint $M$ is calculated as:

$$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$$

Steps:

1. Add the x-coordinates of the two points and divide by 2 → This gives the x-coordinate of the midpoint.

2. Add the y-coordinates of the two points and divide by 2 → This gives the y-coordinate of the midpoint.

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Examples:

Example 1: Simple Numbers

Points: $A(2,4)$ and $B(6,8)$Find the midpoint.

Solution:

1. x-coordinate of midpoint:

   $$\frac{2+6}{2}=\frac{8}{2}=4$$

2. y-coordinate of midpoint:

   $$\frac{4+8}{2}=\frac{12}{2}=6$$

3. Midpoint: $(4,6)$

Verification:

• The midpoint is exactly in the middle of (2,4) and (6,8).