question_answer

The coordinates of the mid-points of the sides of a triangle are (4, 2), (3, 3) and (2, 2). What will be the coordinates of the centroid of the triangle?

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

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

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

D)  \[\left( -3,\frac{7}{3} \right)\]

Correct Answer: A

Solution :

Let PQR be a triangle and A (4, 2), B (3, 3) and C (2, 2) be the mid-points of sides PQ, PR and QR respectively.    Now, G is the centroid of triangle PQR. Also, G (x, y) is the centroid of triangle formed by joining A, B and C.             \[\therefore \]  \[x=\frac{4+3+2}{3}=\frac{9}{3}\] and \[y=\frac{3+2+2}{3}=\frac{7}{3}\] \[\Rightarrow \]            \[G=\left( 3,\frac{7}{3} \right)\]