Question

A triangle has corners at `(1 ,9 )`, `(3 ,4 )`, and `(4 ,5 )`. How far is the triangle's centroid from the origin?

Answer 1

≈ 6.566 units.

Explanation:

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

`x_c=1/3(x_1+x_2+x_3)" and " y_c=1/3(y_1+y_2+y_3)`

That is the average of the coordinates of the vertices.

substituting the given coordinates into the above.

`x_c=1/3(1+3+4)=8/3" and " y_c=1/3(9+4+5)=6`

`rArr"coordinates of centroid" =(8/3,6)`

To calculate the distance from this point to the origin use `color(blue)"Pythagoras' theorem"`

`d=sqrt((8/3)^2+6^2)=sqrt(64/9+324/9)`

`=sqrt(388/9)≈6.566" to 3 decimal places"`