You seem to be making a bit of a meal out of this one.Originally Posted byJameson

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.

RonL