Difference between revisions of "Midpoint"
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== Definition == | == 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. | ||
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== See Also == | == See Also == | ||
* [[Bisect]] | * [[Bisect]] | ||
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+ | {{stub}} | ||
[[Category:Definition]] | [[Category:Definition]] | ||
[[Category:Geometry]] | [[Category:Geometry]] |
Revision as of 02:36, 12 February 2021
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.
Midpoints and Triangles
Midsegments
As shown in Figure 2, is a triangle with , , midpoints on , , respectively. Connect , , (segments highlighted in green). They are midsegments to their corresponding sides. Using SAS Similarity Postulate, we can see that and likewise for and . Because of this, we know that Which is the Triangle Midsegment Theorem. Because we have a relationship between these segment lengths, with similar ratio 2:1. The area ratio is then 4:1; this tells us
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:
See Also
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