Question

A triangle has corners at `(5 ,6 )`, `(4 ,7 )`, and `(3 ,9 )`. How far is the triangle's centroid from the origin?

Answer 1

Distance of centroid from origin is `8.353`

Explanation:

Coordinates of centroid of a triangle whose vertices (corners) 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)`

As corners of triangle are `(5,6)`, `(4,7)` and `(3,9)`, the centroid of given triangle is `((5+4+3)/3,(6+7+9)/3` or `(4,22/3)`.

And its distance from origin is `sqrt((4-0)^2+(22/3-0)^2)=sqrt(16+484/9)`

= `sqrt((144+484)/9)=sqrt(628/9)=2/3sqrt157=2/3xx12.53=8.353`