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
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
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:
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