Question

A triangle has corners at `(2 ,9 )`, `(4 ,8 )`, and `(5 ,3 )`. How far is the triangle's centroid from the origin?

Answer 1

Distance from centroid `=7.6" "`units

Explanation:

Solve the centroid `C(x_c, y_c)` first

`x_c=(x_1+x_2+x_3)/3=(2+4+5)/3=11/3`
`y_c=(y_1+y_2+y_3)/3=(9+8+3)/3=20/3`

Solve distance `d` from the origin using `(x_c, y_c)` and `(0, 0)`

`d=sqrt((x_c-0)^2+(y_c-0)^2)`

`d=sqrt((11/3-0)^2+(20/3-0)^2)`

`d=7.608474807" "`units