Answer: Choice B.
(x,y) --> (x, y-2)
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Step-by-step explanation:
Choice A can be ruled out because of the jump from x to 2x, and from y to 2y. This is a dilation with a scale factor 2. Meaning the preimage enlarges to a bigger image. Specifically the larger image has side lengths twice as long as the smaller preimage. The larger image of course cannot possibly be congruent to the smaller preimage. Congruent figures must have the same corresponding side lengths.
We'll come back to choice B.
Choice C and choice D are ruled out for similar reasoning as choice A was eliminated.
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To summarize the previous section: We ruled out choices A, C, and D. The only thing left is choice B.
Choice B is a translation. The jump from y to y-2 means we shift the point 2 units down. There is no left or right shifting because x stays the same.
For example, the point (5,12) moves to (5,10).
Notice that dilation is not being applied for choice B.
With any geometric translation, aka shifting, the side lengths will remain intact. Something that is 5 units long will stay 5 units long. No amount of shifting will change the distance.
Therefore, a translation preserves distances and lengths. We consider it a rigid transformation. This is why choice B will have the preimage congruent to the image.