Midpoint: Difference between revisions
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== Definition == | |||
The '''midpoint''' of a [[line segment]] is the [[point]] on the segment equidistant from both endpoints. | The '''midpoint''' of a [[line segment]] is the [[point]] on the segment equidistant from both endpoints. | ||
A midpoint [[bisect]]s the line segment that the midpoint lies on. Because of this property, we say that for any line segment <math>\overline{AB}</math> with midpoint <math>M</math>, <math>AM=BM=\frac{1}{2}AB</math>. Alternatively, any point <math>M</math> on <math>\overline{AB}</math> such that <math>AM=BM</math> is the midpoint of the segment. | |||
<asy> | |||
draw((0,0)--(4,0)); | |||
dot((0,0)); | |||
label("A",(0,0),N); | |||
dot((4,0)); | |||
label("B",(4,0),N); | |||
dot((2,0)); | |||
label("M",(2,0),N); | |||
</asy> | |||
== In Cartesian Plane == | |||
In the Cartesian Plane, the coordinates of the midpoint <math>M</math> can be obtained when the two endpoints <math>A</math>, <math>B</math> of the line segment <math>\overline{AB}</math> is known. Say that <math>A: A(x_A,y_A)</math> and <math>B: B(x_B,y_B)</math>. The Midpoint Formula states that the coordinates of <math>M</math> can be calculated as: | |||
<cmath>\begin{align*} | |||
M(\frac{x_A+x_B}{2}&,\frac{y_A+y_B}{2}) | |||
\end{align*}</cmath> | |||
== See Also == | == See Also == | ||
* [[Bisect]] | * [[Bisect]] | ||
Revision as of 22:42, 11 February 2021
This article is a stub. Help us out by expanding it.
Definition
The midpoint of a line segment is the point on the segment equidistant from both endpoints.
A midpoint bisects the line segment that the midpoint lies on. Because of this property, we say that for any line segment 
with midpoint 
, 
. Alternatively, any point on such that 
is the midpoint of the segment.
![[asy] draw((0,0)--(4,0)); dot((0,0)); label("A",(0,0),N); dot((4,0)); label("B",(4,0),N); dot((2,0)); label("M",(2,0),N); [/asy]](http://latex.artofproblemsolving.com/5/7/1/571a5caf94ee7510f23a179e0cdd7dd723b82020.png)
In Cartesian Plane
In the Cartesian Plane, the coordinates of the midpoint can be obtained when the two endpoints 
, 
of the line segment is known. Say that 
and 
. The Midpoint Formula states that the coordinates of can be calculated as:
