Pronunciation: /ˈmɪdˌpɔɪnt/ ?
A midpoint is a point
between two points. The midpoint is on the line segment joining the two points
and divides the line segment exactly in half. The exact mathematical definition is:
A midpoint M between points A and B
is a point such that AM = MB.
Constructing a Midpoint
||Start with the points A and B.|
||Draw the line segment .|
||Draw a circle with center at A and radius AB.|
||Draw a circle with center at B and radius AB|
||Mark one intersection of the two circles as point C and the other intersection of the two circles as pointD.|
||Draw the line segment .|
||Mark the point of intersection of line segment and line segment as M. Point M is the midpoint.|
|Table 1: Constructing a midpoint.|
Calculate a Midpoint in a 1-Dimensional Space
|Manipulative 1: Midpoint on a number line. Click on the blue points and drag them to change the figure. Double click on the manipulative to view it full screen.||
The formula for a midpoint in a one dimensional space between A and B is
. Click on the
blue points in manipulative 1 and drag them to change the figure.
Calculate a Midpoint in a 2-Dimensional Space
|Manipulative 2: Calculating a midpoint in 2-dimensional space.
A midpoint divides the line segment exactly in half. This fact can be used
to figure out the formula for a midpoint of a line segment in a 2-dimensional
Euclidean space such as a Cartesian coordinate system. The x-coordinate of
the midpoint will be halfway between the x-coordinates of the two points, and
the y-coordinate of the midpoint will be halfway between the y-coordinates of
the two points. The formula for the midpoint of a line segment with end-points
Calculating a Midpoint in n-Dimensional Space
The algorithm for calculating an endpoint in 2-dimensional
space can be generalized for n-Dimensional Space. Given two points
the midpoint is
Proof: If M is the midpoint of
This proof is a paragraph proof or informal proof.
The definition of the midpoint of a segment is that .
In other words, the lengths of the two segments are equal. By the definition of
is congruent with
if and only if
have the same measure. Since, by the definition of a midpoint,
have the same measure,
- midpoint. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=midpoint&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
Cite this article as:
Midpoint. 2010-03-22. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/m/midpoint.html.
2010-03-22: Added information on constructing a midpoint, calculating a midpoint in 1 dimension, and calculating a midpoint in n dimensions. (McAdams, David.
2009-12-18: Added "References" (McAdams, David.
2008-10-07: Initial version (McAdams, David.