Midpoints (Algebra)
The midpoint is the point on a line segment that divides it into two equal parts.
The midpoint formula is as follows:
![](data:image/png;base64,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)
Example
The endpoints of a line are (4, 8) and (4, 0). Find the coordinates of the midpoint.
Plug the points into the midpoint formula:
x:
((4 + 4) / (2))
= 4
y:
((8+0) / (2))
= 4
Therefore the midpoint is (4, 4)
The midpoint formula is as follows:
Example
The endpoints of a line are (4, 8) and (4, 0). Find the coordinates of the midpoint.
Plug the points into the midpoint formula:
x:
((4 + 4) / (2))
= 4
y:
((8+0) / (2))
= 4
Therefore the midpoint is (4, 4)