coordinates of midpoint

The coordinates of the midpointMathworldPlanetmathPlanetmathPlanetmath of a line segmentMathworldPlanetmath are the arithmetic meansMathworldPlanetmath of the coordinates of the endpointsMathworldPlanetmath of the segment. Thus, if the endpoints are  (x1,y1)  and  (x2,y2),  then the midpoint is


For justifying the above coordinates of the midpoint, we know that its abscissaMathworldPlanetmath x0 halves on the x-axis the line segment between x1 and x2. Since the lengths of the half-segments are x0-x1 and x2-x0, if  x1<x2,  and their opposite numbers, if  x2<x1,  in any case we can write


Solving this equation for x0 yields:  x0=x1+x22.  result is gotten for the ordinate of the midpoint.

Title coordinates of midpoint
Canonical name CoordinatesOfMidpoint
Date of creation 2013-03-22 17:31:07
Last modified on 2013-03-22 17:31:07
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 5
Author pahio (2872)
Entry type Result
Classification msc 51N20
Classification msc 51M15
Classification msc 51-00
Related topic ConjugateDiametersOfEllipse
Related topic CentreOfMassOfPolygon
Related topic Midpoint4