In the above graph, shape ABCDE is rotated 45 degrees counterclockwise around point D", and then shape A'B'C'D'E' is translated along a vector {4.84,2.83}. Refer to the worksheets specifically proving translations and rotations without coordinate grids. To prove this composition with a coordinate grid would be achieved the same way as it would be without a coordinate grid because of the coordinates of the points being decimals. When the points on a shape in a coordinate grid do not land on an intersection of grid lines, than the problem is solved as if there were no gird lines. This is because the problem cannot simply be solved by counting and doing pythagorean theorem (for translations) or using coordinate notation (for rotations).