What is the Midpoint Formula?

Hand touching two points on digital ruler
Hand touching two points on digital ruler. Paper Boat Creative / Getty Images
By
Deb Russell
Deb Russell
Math Expert
Deb Russell is a school principal and teacher with over 25 years of experience teaching mathematics at all levels.
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Updated on September 03, 2019

The midpoint formula is applied when one is required to find the exact center point between two defined points. So for a line segment, use this formula to calculate the point that bisects a line segment defined by the two points. 

The Midpoint Formula: Definition of Midpoint

The midpoint is a give-away with its name. What is the exact halfway point between two points? Hence the name midpoint.

A visual for the Midpoint Formula

The lines through P1 and P2, parallel to the y-axis intersect the x-axis at A1(x1,0) and A2(x2,0). The The midpoint through M parallel to the y-axis bisects the segment A1A2 at point M.

M1 is halfway form A1 to A2, the x-coordinate of M1 is:

x1 + 1/2 ( x2 - x1) = x1 + 1/2 x2 - 1/2 x1

= 1/2 x1 + 1/2 x2

=( x1 + x2) ÷ 2 

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Russell, Deb. "What is the Midpoint Formula?" ThoughtCo, Aug. 27, 2020, thoughtco.com/geometry-midpoint-formula-2312239. Russell, Deb. (2020, August 27). What is the Midpoint Formula? Retrieved from https://www.thoughtco.com/geometry-midpoint-formula-2312239 Russell, Deb. "What is the Midpoint Formula?" ThoughtCo. https://www.thoughtco.com/geometry-midpoint-formula-2312239 (accessed May 30, 2023).