What are midpoints of a segment?

The midpoint of a segment is the point that divides the segment into two equal parts. It is located at the average of the coordinates of the endpoints of the segment. For a segment with endpoints at coordinates (x₁, y₁) and (x₂, y₂), the midpoint can be calculated using the formula ((\frac{x₁ + x₂}{2}, \frac{y₁ + y₂}{2})). This point is crucial in geometry for various constructions and proofs.