question_answer

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

A) \[\left( \frac{1}{3},\frac{7}{3} \right)\]                      

B) \[\left( 1,\frac{7}{3} \right)\]

C) \[\left( -\frac{7}{3},\frac{7}{3} \right)\]                    

D) \[\left( -1,\frac{7}{3} \right)\]

Correct Answer: B

Solution :

Let D and £ are the mid points of AB and AC. So, the coordinates of B and C are (- 3, 3) and (5, 3) respectively, Centroid of triangle \[=\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3} \right)\] \[=\left( \frac{1-3+5}{3},\frac{1+3+3}{3} \right)\] \[=\left( 1,\frac{7}{3} \right)\]