Question

A triangle has corners at `(5 ,1 )`, `(7 ,2 )`, and `(6 ,3 )`. How far is the triangle's centroid from the origin?

Answer 1

Centroid is 6.3246 from the origin

Explanation:

Coordinates of Centroid of a triangle is obtained as below :
Let G be the centroid and the coordinates G(x), G(y).

X coordinate of centroid `Gx) = (x_1 + x_2 + x_3) / 3` &
Y coordinate of centroid `G(y) = (y_1 + y_2 + y_3) / 3`

`G(x) = (5 + 7 + 6) / 3 = 6`

`G(y) = (1 + 2 + 3) / 3 = 2`

Distance ‘ D’ of centroid ‘G’ from origin is given by
`D = sqrt((G(x) - 0)^2 + (G(y) - 0)^2)`

`D = sqrt(G(x)^2 + G(y)^2) = sqrt(6^2 + 2^2) = sqrt (40) = 6.3246`