Assuming that the figure is rotated about the origin, a rotation of 180° is described by the rule:
[tex](x,y)\rightarrow(-x,-y)[/tex]The coordinates of the point C are (4,7). Then, after a rotation of 180°:
[tex](4,7)\rightarrow(-4,-7)[/tex]Therefore, the coordinates of C' would be:
[tex](-4,-7)[/tex]