You seem to be making a bit of a meal out of this one.Originally Posted by Jameson
The region is a triangle symmetric about the y-axis, with a vertex at (0,0)
and the two other vertices on the line y=3.
So the centre of mass is on the axis of symmetry x=0, also it cannot be at
either (0,0) or (0,3), as these are a vertex and on a side respectively.
Also it cannot be at (0,1), as this leaves much more area above than below
the line y=1.
So we conclude that the centre of mass must be at (0,2) if it is at any of the
given candidate answers.