question_answer

The centroid of the triangle formed by the lines\[x=0,x-y=3\]and\[2x+3y=6\]is

A)  \[(3,-1)\]

B)  \[(1,-3)\]

C)  \[\left( 1,\frac{1}{3} \right)\]

D)  \[\left( 1,-\frac{1}{3} \right)\]

Correct Answer: D

Solution :

 The coordinates of vertices are A (3,0), B(0,2) and\[C(0,-3)\] Hence, centroid of triangle \[=\left( \frac{3+0+0}{3},\frac{0+2-3}{3} \right)\] \[=\left( 1,-\frac{1}{3} \right)\]