Can anybody explain and answer this thoroughly?

Answer: Choice B (31, 52)

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Explanation:

To go from the point (1,2) to (4,7) we do two things:
A) Move 3 units to the right
B) Move 5 units up

Applying the scale factor will multiply those movement steps by 10. So instead of "3 units to the right" we'll go "30 units to the right" since 3*10 = 30. Similarly, we'll move 50 units up instead of 5 (5*10 = 50)

So if we start at (1,2) and move 30 units to the right and 50 units up, then we'll land on (31, 52) which is the image point for the preimage (4,7)

This is why the answer is choice B

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Note: We can alternatively shift both initial points to the left 1 and down 2 so that (1,2) lands on the origin (0,0). That means (4,7) turns into (3,5). Apply the scale factor through multiplying both coordinates by 10. This works only because the reference point is the origin. We end up with (30,50). Now undo the "left 1 and down 2" to "move right 1, up 2" and we arrive at (31,52) which is the same answer as before. So this is further confirmation that the answer is choice B