To determine how the figure is moved based on the translation rule [tex]\((x, y) \rightarrow (x-3, y+6)\)[/tex], follow these steps:
1. Understand the translation rule:
The given rule is [tex]\((x, y) \rightarrow (x-3, y+6)\)[/tex]. This rule tells us how each point [tex]\((x, y)\)[/tex] on the figure is translated to a new point.
2. Analyze the x-coordinate:
- The rule for the x-coordinate is [tex]\(x \rightarrow x-3\)[/tex].
- We see that [tex]\(3\)[/tex] units are subtracted from the x-coordinate.
- Subtracting [tex]\(3\)[/tex] means moving left by [tex]\(3\)[/tex] units.
3. Analyze the y-coordinate:
- The rule for the y-coordinate is [tex]\(y \rightarrow y+6\)[/tex].
- We see that [tex]\(6\)[/tex] units are added to the y-coordinate.
- Adding [tex]\(6\)[/tex] means moving up by [tex]\(6\)[/tex] units.
4. Describe the movement:
Based on the points above, we can determine the overall movement of the figure:
- For the x-coordinate: The figure moves left by [tex]\(3\)[/tex] units.
- For the y-coordinate: The figure moves up by [tex]\(6\)[/tex] units.
Given these observations, the correct description of the movement is:
left 3 units and up 6 units.
