Question 1091733: For the transformation T, write the inverse T-1.
T: (x, y) --> ( 2x, y + 5)
T-1: (x, y)-->
A.) (x - 2, y - 5)
B.) (½x, y - 5)
C.) (2x - 1, y + 4)
Please explain. Thank you.
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! T takes the x value and doubles it and adds 5 to the y value.
So T's inverse, would take half of the x value and subtract 5 from the y value.
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! For the transformation T, write the inverse T-1.
T: (x, y) --> (2x, y + 5)
T-1 (x, y)-->
A.) (x - 2, y - 5)
B.) (½x, y - 5)
C.) (2x - 1, y + 4)
The inverse of T, written T-1, does the exact opposite to
the coordinates as T does to them.
Transform T changes x to 2x, which is to double the first coordinate.
The opposite of doubling the first coordinate is halving the first
coordinate, so T-1 takes x to ½x
Transform T also takes y to y+5, which is adding 5 to the second coordinate.
The opposite of adding 5 to the second coordinate is subtracting 5 from
the second coordinate, so T-1 takes y to y-5.
Therefore,
T-1: (x, y)--> (½x, y-5)
Correct answer is B.
Edwin
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