KnowraMidpointMidpointA midpoint is the point exactly halfway between two endpoints on a line segment, equidistant from both endpoints.BriefConnectLine segment: A portion of a line bounded by two endpoints. A midpoint divides this bounded portion into two equal lengths.Midpoint formula: A rule for finding the coordinates halfway between two points by averaging corresponding coordinates. It turns the equal-distance definition into a direct calculation.Perpendicular bisector: A line that meets a segment at its midpoint at a right angle. Its defining intersection is the segment’s midpoint.Endpoint: A point at either boundary of a line segment. Unlike an endpoint, the midpoint lies inside the segment and is equally distant from both boundaries.Distance: A measure of the separation between two points. The midpoint is characterized by equal distances to both endpoints.Arithmetic mean: The sum of a set of numbers divided by the number of values. Each coordinate of a midpoint is the arithmetic mean of the endpoint coordinates.Midsegment: A segment joining the midpoints of two sides of a triangle or trapezoid. Midpoints of sides generate special segments with predictable lengths and parallelism.Median: A line segment from a triangle vertex to the midpoint of the opposite side. The median is a segment through a midpoint, not the midpoint itself.Coordinate geometry: The study of geometric objects using coordinates and algebra. Coordinates provide a numerical way to locate a midpoint.Vector addition: An operation that combines vectors by adding their corresponding components. A midpoint vector can be found by adding endpoint position vectors and halving.Show all 19Linked from 15 pagesMazur–Ulam theoremBroader topic: Preserving midpoints is the key intermediate conclusion of the theorem.Bisection methodRelated: Each iteration tests the midpoint and divides the current bracket into equal halves.Nine-point circleNarrower topic: Three side midpoints and three vertex–orthocenter midpoints lie on the circle.Segment Addition PostulateBroader topic: Applying segment addition to a midpoint gives two equal parts whose sum is the whole.Sierpiński triangleRelated: Joining the side midpoints identifies the central triangle removed at each stage.Butterfly theoremNarrower topic: Both the given chord and the segment between chord midpoints are bisected.Euler's quadrilateral theoremRelated: The correction term is four times the squared distance between the two diagonal midpoints.Midpoint theoremNarrower topic: The theorem begins by selecting the halfway point on each of two triangle sides.Show all 15