What is the Midpoint Formula?

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

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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 A_1A2 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