Question

A triangle has corners at `(7 ,1 )`, `(8 ,2 )`, and `(5 ,9 )`. How far is the triangle's centroid from the origin?

Answer 1

The distance of centroid from the origin is `7.77(2dp)` unit

Explanation:

The co-ordinate of centroid of the triangle is`x=(x_1+x_2+x_3)/3=(7+8+5)/3=20/3, y=(y_1+y_2+y_3)/3=(1+2+9)/3=4`i.e `(20/3,4)`; The distance of centroid`(20/3,4)` from the origin`(0,0)` is `sqrt((20/3-0)^2+(4-0)^2)=sqrt(400/9+16)=sqrt(544/9)=7.77(2dp)`unit[Ans]