In the `DeltaABC`, the coordinates of B are `(0, 0), AB=2, /_ABC=pi/3` and the middle point of BC has the coordinates (2,0). The centroid of the triangle is

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))`.