In ` A B C ,` the coordinates of `B` are `(0,0),A B=2,/_A B C=pi/3,` and the middle point of `B C` has coordinates `(2,0)dot` The centroid o the triangle is `(1/2,(sqrt(3))/2)` (b) `(5/3,1/(sqrt(3)))` `(4+(sqrt(3))/3,1/3)` (d) none of these

Options

A. `(1//2,sqrt3//2)`
B. `(5//3,1//sqrt3)`
C. `(4+sqrt3//3,1//3)`
D. none of these

Answer

B

Explanation

`(2,0)` is the midpoint of B(0,0) and C. Then C has coordinates (4,0). Also, A has coordinates `(0+2cospi//3,0+2sinpi//3)-=(1,sqrt(3))`. Then the centroid is `(5//3,1sqrt(3))`.