The Proof of the Midpoint Formula

Introduction

The midpoint is the middle point of a segment. It is equidistant from both end points. The midpoint formula is used to determine the coordinates of the midpoint of a segment. This formula is familiar to middle school and high school students, however most books do not discuss its proof. In this post, we discuss the mathematical proof of the midpoint formula.

Midpoint

The slope and distance formulas are needed to prove the midpoint formula. Recall that the slope $latex m$ of the line containing the two points $latex P$ and $latex Q$ with coordinates $latex (a,b)$ and $latex (c,d)$ respectively isĀ  Continue reading