Question

What is the centroid of a triangle with corners at `(4, 7 )`, `(1,2 )`, and `(8 , 5 )`?

Answer 1

Centroid of the triangle is`(4 1/3,4 2/3)`

Explanation:

he centroid of a triangle whose vertices are `(x_1,y_1)`, `(x_2,y_2)` and (x_3,y_3)# is given by

`((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`

Hence centrid of given triangle is `((4+1+8)/3,(7+2+5)/3)` or `(13/3,14/3)` or `(4 1/3,4 2/3)`.

[For detailed proof for the formula see here.](http://www.learnnext.com/nganswers/ask-question/answer/How-to-derive-the-formula-of-centroid-from-section-formula/Coordinate-Geometry/84881.htm)