Jump to content

Talk:Section formula

Page contents not supported in other languages.
From Wikipedia, the free encyclopedia

Someone Deleted this

[edit]

Coordinates of centroid

[edit]
Centroid of a triangle

The centroid of a triangle is the intersection of the medians and divides each median in the ratio . Let the vertices of the triangle be , and . So, a median from point A will intersect BC at . Using the section formula, the centroid becomes:

Coordinates of incenter

[edit]

Let the sides of a triangle be , and its vertices are , and . The Incentre (intersection of the angle bisectors) divides the angle bisectors in the ratio , and . An angle bisector also divides the opposite side in the ratio of the adjacent sides (Angle bisector theorem). So they meet at . Thus, the incenter is

This is essentially the weighted average of the vertices.

Shubhrajit Sadhukhan (talk) 13:25, 7 November 2020 (UTC)[reply]