Answer:
D, B, C; see attached
Explanation:
You want to identify the transformations from Figure A to each of the other figures.
a. Translation
A translated figure has the same orientation (left-right, up-down) as the original figure. Figure D is a translation of Figure A. The arrow of translation joins corresponding points.
b. Reflection
A figure reflected across a vertical line has left and right interchanged. Up and down remain unchanged. Figure B is a reflection of Figure A. The line of reflection is the perpendicular bisector of the segment joining corresponding points.
c. Rotation
A rotated figure keeps the same clockwise/counterclockwise orientation, but has the angle of any line changed by the same amount relative to the axes. Figure C is a 180° rotation of Figure A. The center of rotation is the midpoint of the segment joining corresponding points. Unless the figures overlap, the center of rotation is always outside the figure.
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Additional comment
The center of rotation is the coincident point of the perpendicular bisectors of the segments joining corresponding points on the figure. It will be an invariant point, so will only be on or in the figure of the figures touch or overlap. In the attachment, the center of rotation is shown as a purple dot.