Question

A triangle has corners at `(5 ,2 )`, `(9 ,7 )`, and `(6 ,5 )`. How far is the triangle's centroid from the origin?

Answer 1

Distance of Centroid G from origin O is `color(green)(GO = 8.1377)`

Explanation:

`G_x = (5 + 9 + 6) / 3 = 20/3`

`G_y = (2 + 7 + 5) / 3 = 14/3`

To find the distance `G(20/3, 14/3)` to `O (0, 0)` where G is the centroid and O the origin.

`GO = d = sqrt(((20/3) -0)^2 + ((14/3)-0)^2) = 8.1377`