If the point $G (-4,6)$ was moved horizontally 4 units to the left, which of the following is the correct mapping to the translation?
A. $(x, y) \rightarrow(x, y+4)$
B. $(x, y) \rightarrow(x+4, y)$
C. $(x, y) \rightarrow(x, y-4)$
D. $(x, y) \rightarrow(x-4, y)$
Answer (1)
A horizontal translation to the left affects the x-coordinate.
Moving 4 units to the left means subtracting 4 from the x-coordinate.
The mapping is ( x , y ) → ( x − 4 , y ) .
The correct mapping is ( x , y ) → ( x − 4 , y ) .
Explanation
Analyze the problem The problem asks us to find the correct mapping for a horizontal translation of a point 4 units to the left. This means we need to adjust the x-coordinate of the point while keeping the y-coordinate the same.
Determine the mapping A horizontal translation to the left means we subtract from the x-coordinate. Since we are moving 4 units to the left, we subtract 4 from the x-coordinate. Therefore, the mapping is ( x , y ) → ( x − 4 , y ) .
Verify the mapping Let's test this mapping with the given point G ( − 4 , 6 ) . Applying the mapping, we get ( − 4 − 4 , 6 ) = ( − 8 , 6 ) . This confirms that the x-coordinate is indeed shifted 4 units to the left, and the y-coordinate remains unchanged.
State the final answer The correct mapping is ( x , y ) → ( x − 4 , y ) .
Examples
Imagine you are designing a game where a character needs to move left on the screen. If the character's initial position is (x, y), and you want to move them 4 steps to the left, you would apply the translation (x, y) -> (x - 4, y). This ensures the character moves horizontally without changing their vertical position.
