21. If a vertex of a triangle is (1, 1) and the midpoints of two sides of the triangle through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle isA. `((1)/(3),(7)/(3))`B. `(2,(7)/(3))`C. `(-(1)/(3),(7)/(3))`D. `(-1,(7)/(3))`

21. If a vertex of a triangle is (1, 1) and the midpoints of two sides

1.	21. If a vertex of a triangle is (1, 1) and the midpoints of two sides of the triangle through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle isA. `((1)/(3),(7)/(3))`B. `(2,(7)/(3))`C. `(-(1)/(3),(7)/(3))`D. `(-1,(7)/(3))`
Answer» Correct Answer - B 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))`

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