- Midpoint
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The midpoint (also known as class mark in relation to histogram) is the middle point of a line segment. It is equidistant from both endpoints.
Contents
Formulas
The formula for determining the midpoint of a segment in the plane, with endpoints (x1) and (x2) is:
The formula for determining the midpoint of a segment in the plane, with endpoints (x1, y1) and (x2, y2) is:
The formula for determining the midpoint of a segment in the space, with endpoints (x1, y1, z1) and (x2, y2 z2) is:More generally, for an n-dimensional space with axes , the midpoint of an interval is given by:
Construction
The midpoint of a line segment can be located by first constructing a lens using circular arcs, then connecting the cusps of the lens. The point where the cusp-connecting line intersects the segment is then the midpoint. It is more challenging to locate the midpoint using only a compass, but it is still possible.[1]
See also
References
- ^ "Wolfram mathworld". 29 September 2010. http://mathworld.wolfram.com/Midpoint.html.
External links
- Animation - showing the characteristics of the midpoint of a line segment
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