Question
11. Use the ordered pair transtation rule \( (x, y)=(x-2 , y+5) \) to find the preimage of \( (0,12) \). Type an ondered pair for the preimage. \( \square \) (Type an ordered pair.)
Ask by Gordon Bartlett. in the United States
Feb 25,2025
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Tutor-Verified Answer
Answer
The preimage is (2, 7).
Solution
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The Deep Dive
To find the preimage using the translation rule \( (x, y)=(x-2 , y+5) \), you need to reverse the transformations applied to the ordered pair \( (0,12) \). Starting with \( (0, 12) \): 1. For \( x \), you set up the equation: \( x - 2 = 0 \) which gives \( x = 2 \). 2. For \( y \), you set up the equation: \( y + 5 = 12 \) which gives \( y = 7 \). Thus, the preimage of \( (0, 12) \) is \( (2, 7) \). So the ordered pair is \( (2, 7) \).