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 P_{1} and P_{2}, parallel to the y-axis intersect the x-axis at A_{1}(x_{1},0) and A_{2}(x_{2},0). The The midpoint through M parallel to the y-axis bisects the segment A_{1A2} at point M.

M_{1} is halfway form A_{1} to A_{2}, the x-coordinate of M_{1} is:

x_{1} + 1/2 ( x_{2} - x_{1}) = x_{1} + 1/2 x_{2} - 1/2 x_{1}

= 1/2 x_{1} + 1/2 x_{2}

=( x_{1} + x_{2}) ÷ 2