A square on a coordinate plane is translated 9 units down and 1 unit to the right. Which function rule describes the translation?
A. [tex]T_{1,-9}(x, y)[/tex]
B. [tex]T_{-1,-9}(x, y)[/tex]
C. [tex]T_{-9,1}(x, y)[/tex]
D. [tex]T_{-9,-1}(x, y)[/tex]
Answer (2)
The translation 1 unit to the right is represented by adding 1 to the x-coordinate.
The translation 9 units down is represented by subtracting 9 from the y-coordinate.
The function rule is therefore T ( x , y ) = ( x + 1 , y − 9 ) .
The function rule that describes the translation is T 1 , − 9 ( x , y ) .
Explanation
Analyze the problem The problem describes a translation of a square on a coordinate plane. The square is moved 9 units down and 1 unit to the right. We need to determine the function rule that represents this translation.
Determine the translation rule A translation involves shifting a geometric figure without changing its size or orientation. A translation of 1 unit to the right means we add 1 to the x-coordinate. A translation of 9 units down means we subtract 9 from the y-coordinate. Therefore, the translation rule can be written as:
T ( x , y ) = ( x + 1 , y − 9 )
Express the rule using given notation The translation rule T ( x , y ) = ( x + 1 , y − 9 ) is equivalent to the notation T 1 , − 9 ( x , y ) . This notation indicates a translation where the x-coordinate is increased by 1 and the y-coordinate is decreased by 9.
State the final answer The function rule that describes the translation is T 1 , − 9 ( x , y ) .
Examples
Imagine you're designing a video game where a character needs to move across the screen. If you want the character to move 1 step to the right and 9 steps down with each button press, you would use this translation. This ensures the character moves consistently and predictably with each input.
The translation of the square involves moving it 1 unit to the right and 9 units down. Therefore, the function rule that describes this translation is T 1 , − 9 ( x , y ) . The correct answer is option A.
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