Perform the requested transformation on the CENTER of the circle. Since all of the transformations you are required to perform are "isometries," pre-image distances are preserved in the image, so the image circle will have a radius equal to the radius in the pre-image circle. Once you know where the image of the center is, just draw the image circle.
For example, the center of the pre-image circle is at (2, 2). If you perform the translation T(3, 5), image of the center will be at (2 + 3, 2 + 5), or (5, 7). The radius of the pre-image circle is 2 units, so the radius of the image circle will be 2 units also. Using (5, 7) as the center, draw a circle with radius 2 units and that will be the image of the circle under the translation T(3, 5).
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