Final answer:
The correct algebraic rule for translating a figure three units right and seven units down is (x + 3, y - 7).
Step-by-step explanation:
The algebraic rule to translate a figure three units right and seven units down is represented by adding 3 to the x-coordinate and subtracting 7 from the y-coordinate. Therefore, the correct answer is (x + 3, y - 7). When you translate a point to the right, you increase the x-coordinate, and when you translate a point down, you decrease the y-coordinate.