Question

A triangle has corners at `(7 ,6 )`, `(8 ,2 )`, and `(5 ,9 )`. How far is the triangle's centroid from the origin?

Answer 1

`≈8.75" units"`

Explanation:

The first step is to establish the position of the centroid.

Given `(x_1,y_1),(x_2,y_2)" and " (x_3,y_3)` are the vertices of a triangle, then.

`x_c=1/3(x_1+x_2+x_3)` and

`y_c=1/3(y_1+y_2+y_3)`

`rArrx_c=1/3(7+8+5)=20/3`

and `y_c=1/3(6+2+9)=17/3`

`rArr" coordinates of centroid " =(20/3,17/3)`

To calculate the distance (d) from the origin to the centroid, use `color(blue)"Pythagoras' theorem"`

`d=sqrt((20/3)^2+(17/3)^2)=sqrt((400/9)+(289/9))`

`=sqrt(689/9)≈8.75" to 2 decimal places"`