Difference between revisions of "Midpoint"

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{{stub}}
 
{{stub}}
 
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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.
  
The [[Segment Addition Postulate]] states that if <math>M</math> is the midpoint of line segment <math>AB</math>, then <math>AM+MB=AB</math>.
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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.
 
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<asy>
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draw((0,0)--(4,0));
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dot((0,0));
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label("A",(0,0),N);
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dot((4,0));
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label("B",(4,0),N);
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dot((2,0));
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label("M",(2,0),N);
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</asy>
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== In Cartesian Plane ==
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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:
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<cmath>\begin{align*}
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M(\frac{x_A+x_B}{2}&,\frac{y_A+y_B}{2})
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\end{align*}</cmath>
 
== See Also ==
 
== See Also ==
 
* [[Bisect]]
 
* [[Bisect]]

Revision as of 23:42, 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 $\overline{AB}$ with midpoint $M$, $AM=BM=\frac{1}{2}AB$. Alternatively, any point $M$ on $\overline{AB}$ such that $AM=BM$ 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 $M$ can be obtained when the two endpoints $A$, $B$ of the line segment $\overline{AB}$ is known. Say that $A: A(x_A,y_A)$ and $B: B(x_B,y_B)$. The Midpoint Formula states that the coordinates of $M$ can be calculated as: \begin{align*} M(\frac{x_A+x_B}{2}&,\frac{y_A+y_B}{2}) \end{align*}

See Also

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