If D, E and F are respectively, the mid-points of AB, AC and BC in `DeltaABC`, then BE + AF is equal to

Options

A. `((sqrt(3))/(2), (3)/(2))` and `(sqrt(3),0)`
B. `((sqrt(3))/(2),(1)/(2))` and `(sqrt(3), 0)`
C. `((sqrt(3))/(2), (3)/(2))` and `((sqrt(3))/(2), (1)/(2))`
D. `((3)/(2), (sqrt(3))/(2))` and `((sqrt(3))/(2), (1)/(2))`

Answer

A

Explanation

Clearly, R coincides with the origin O.
`:. RP=OP=2sqrt(3)rArr RF=sqrt(3)`
Hence, coordinates of F are `(sqrt(3),0)`.
`:. RE=RFrArr RE=sqrt(3)`
Hence, the coordinates of E are (RE `cos 60^(@) , "RE" sin 60^(@)`) or `((sqrt(3))/(2), (3)/(2))`