Question

If centroid of the triangle formed by the points $(0,-2),(2,-y)$ and $(1,4)$ is same as the centroid of the triangle formed by the points $(1,0),(x,-3)$ and $(3,1)$, then centroid of the triangle formed by the points $(x,y),(2x-1,-y)$ and $(-x,1-y)$ is

• A. $(2,2)$
• B. $(-2,-2)$
• C. $(1,1)$
• D. $(-1,-1)$

Answer 1

The correct option is D $(-1,-1)$

Centroid of triangle formed by $(0,-2)(2,-y),(1,4)$ is
$(1,\frac{2-y}{3})$

Centroid of triangle formed by $(1,0),(x,-3),(3,1)$ is
$(\frac{x+4}{3},\frac{-2}{3})$
$\therefore (1,\frac{2-y}{3})\equiv (\frac{x+4}{3},-\frac{2}{3})\Rightarrow (x,y)\equiv (-1,4)$
$\therefore (x,y),(2x-1,-y),(-x,1-y)\equiv (-1,4),(-3,-4)(1,-3)$
$\therefore$ Required centroid is $(-1,-1)$