Question

For the transformation T, write the T-1. T: (x, y) ( 2x, y + 5) T -1 (x, y) (x - 2, y - 5) (2x - 1, y + 4) (½x, y - 5)

Answer 1

Answer: Third choice

(½x, y - 5)

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Explanation:

The original transformation (2x, y+5) takes any x value and doubles it. So the inverse of this is to cut the x value in half. We can say x/2 since division is the opposite of multiplication. The value x/2 is the same as ½x

For the y coordinate, we add on 5 for the original transformation. Subtraction undoes addition meaning the inverse will have y-5.

Side note: the inverse notation $T^{-1}$ can be written as T^(-1).