If the point $G(-4,6)$ was moved horizontally 4 units to the left, which of the following is the correct mapping to define the translation?
A. $(x, y) \rightarrow(x, y+4)$
B. $(x, y) \rightarrow(x+4, y)$
C. $(x, y) \rightarrow(x, y-4)$
D. $(x, y) \rightarrow(x-4, y)$

The problem involves a horizontal translation of a point in the coordinate plane.
Moving a point horizontally to the left decreases its x-coordinate.
The y-coordinate remains unchanged during a horizontal translation.
The correct mapping is ( x , y ) → ( x − 4 , y ) .

Explanation

Analyze the problem The problem states that point G ( − 4 , 6 ) is moved horizontally 4 units to the left. We need to determine the correct mapping that defines this translation. A horizontal movement only affects the x-coordinate. Moving to the left means subtracting from the x-coordinate.

Determine the mapping Since the point is moved 4 units to the left, the x-coordinate will change from x to x − 4 . The y-coordinate remains unchanged. Therefore, the correct mapping is ( x , y ) i g h t ha r p oo n u p ( x − 4 , y ) .

State the final answer The correct mapping is ( x , y ) → ( x − 4 , y ) .


Examples
Imagine you are designing a game where a character moves horizontally across the screen. If you want the character to move 4 steps to the left, you would apply the translation ( x , y ) → ( x − 4 , y ) to the character's coordinates. This ensures the character moves the correct distance in the desired direction, making the game interactive and responsive.

Answered by GinnyAnswer | 2025-07-03

The point G(-4,6) moves 4 units to the left, changing its x-coordinate while keeping the y-coordinate the same. The correct mapping to describe this translation is ( x , y ) → ( x − 4 , y ) . Therefore, the answer is Option D.
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Answered by Anonymous | 2025-07-04