Geometry - Midpoint Formula

Hand touching two points on digital ruler
Hand touching two points on digital ruler. Paper Boat Creative / Getty Images

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

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 line 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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Your Citation
Russell, Deb. "Geometry - Midpoint Formula." ThoughtCo, Nov. 6, 2017, Russell, Deb. (2017, November 6). Geometry - Midpoint Formula. Retrieved from Russell, Deb. "Geometry - Midpoint Formula." ThoughtCo. (accessed January 23, 2018).