coordinates of midpoint
The coordinates of the midpoint of a line segment
are the arithmetic means
of the coordinates of the endpoints
of the segment. Thus, if the endpoints are (x1,y1) and (x2,y2), then the midpoint is
(x1+x22,y1+y22). |
For justifying the above coordinates of the midpoint, we know that its abscissa 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
x0-x1=x2-x0. |
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 |