If a vertex of a triangle is (1, 1) and the mid-points of two side through this vertex are (-1, 2) and (3, 2), then centroid of the triangle is

Options

A. `((1)/(3),(7)/(3))`
B. `(2,(7)/(3))`
C. `(-(1)/(3),(7)/(3))`
D. `(-1,(7)/(3))`

Answer

B

Explanation

Let ABC to the given triangle whose vertices are `A(1,1) B(x_(1),B(x_(1),y_(2))`. Let D(-1,2), and E(3,2) be the mid -points of AB and AC respecvtive. Then,
`(x_(1)|1)/(2)=-1,(y_(1)|1)/(2)=2,(x_(2)|1)/(2)=3 and (y_(2)+1)/(2)=2`
`rArr x_(1)=-3,_(2),y_(1)=3,x_(2)=5 and y_(2)=3`
Thus the coordinates of the vertces of `DeltaABC` are (1,1) B(-3,3) and C(5,3)
`:.` Coordinates of the centorid are `((1-3+5)/(3),(1+3+3)/(3))-=(1,(7)/(3))`