A triangle has corners at (5 ,2 ), (4 ,6 ), and (8 ,5 ). How far is the triangle's centroid from the origin?

1 Answer
Oct 5, 2016

The distance is ~~ 7.13

Explanation:

Centroid coordinates given the vertices is a reference for the equations that I will use.

Let (O_x, O_y) be the centroid and (A_x, A_y), (B_x, B_y), and00 (C_x, C_y) be the vertices then:

O_x = (A_x + B_x + C_x)/3

and

O_y = (A_y + B_y + C_y)/3

O_x = (5 + 4 + 8)/3 = 17/3

and

O_y = (2 + 6 + 5)/3 = 13/3

The distance from the origin is:

d = sqrt((17/3)² + (13/3)²)

d ~~ 7.13