# Difference between revisions of "Midpoint"

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{{stub}} | {{stub}} | ||

− | + | == 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 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 with midpoint , . Alternatively, any point on such that is the midpoint of the segment.

## 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: