Question

A triangle has corners at `(4 ,6 )`, `(3 ,9 )`, and `(7 ,2 )`. How far is the triangle's centroid from the origin?

Answer 1

`7.341\ \text{unit`

Explanation:

Given that the vertices of a triangle are `(x_1, y_1)\equiv(4, 6)`, `(x_2, y_2)\equiv(3, 9)` & `(x_3, y_3)\equiv(7, 2)` then the coordinates of centroid of triangle are given as

`(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3})`

`\equiv (\frac{4+3+7}{3}, \frac{6+9+2}{3})`

`\equiv (14/3, \frac{17}{3})`

hence the distance between the centroid `(14/3, 17/3)` & the origin `(0, 0)` is given by distance formula as follows

`\sqrt{(14/3-0)^2+(17/3-0)^2}`

`=\sqrt{485}/3`

`=7.341\ \text{unit`