Question

A triangle has corners at `(6 ,2 )`, `(4 ,3 )`, and `(5 ,1 )`. How far is the triangle's centroid from the origin?

Answer 1

`\sqrt{29}` units, anout `5.385`.

Explanation:

The centroud of a triangle is obtained from averaging the coordinates of the vertices:

Vertices -- `(color(blue)(6),color(gold)(2)),(color(blue)(4),color(gold)(3)),(color(blue)(5),color(gold)(1))`

Centroid -- `(color(blue)({6+4+5}/3),color(gold)({2+3+1}/3))=(color(blue)(5),color(gold)(2))`.

Then the distance from the origin to point `(a,b)` is `\sqrt{a^2+b^2}`, thus:

`\sqrt{5^2+2^2}=\sqrt{29}`.