Question 1011927
(1) The centroid of a convex polygon is inside the polygon.
Since The x-coordinates of A, B, and C are all positive number,
so will be the x-coordinate of the centroid,
meaning that it will lie to the right of the y-axis.
Another way;
The x-coordinate of the centroid is the average of the x-coordinates of the vertices,
so it is {{{(1+2+c^2)/3=(3+c^2)/3=1+c^2/3>=1}}} ,
so the centroid lies on the line {{{x=1}}} or to its right,
at a distance of at least {{{1}}} to the right of the y-axis.
 
(2) The y-coordinate of the centroid is the average of the y-coordinates of the vertices,
so it is {{{(a+b-3)/3}}} .
For the centroid to be on the x-axis, that y-coordinate must be zero:
{{{(a+b-3)/3=0}}}<-->{{{a+b-3=0}}}<-->{{{highlight(a+b=3)}}} .