To understand the given translation rule \( (x, y) \rightarrow (x-2, y+7) \) for the rectangle, let's analyze what each part of the rule does to the coordinates \( (x, y) \).
1. Translation in the \( x \)-direction:
- The rule \( x \rightarrow x - 2 \) modifies the \( x \)-coordinate of each point.
- Subtracting 2 from the \( x \)-coordinate means moving each point 2 units to the left along the \( x \)-axis.
2. Translation in the \( y \)-direction:
- The rule \( y \rightarrow y + 7 \) modifies the \( y \)-coordinate of each point.
- Adding 7 to the \( y \)-coordinate means moving each point 7 units up along the \( y \)-axis.
Putting these two movements together, we have the complete description of the translation:
- Move every point 2 units to the left.
- Move every point 7 units up.
Therefore, the correct description for the translation \( (x, y) \rightarrow (x-2, y+7) \) is:
- A translation of 2 units to the left and 7 units up.
Thus, the answer is:
- a translation of 2 units to the left and 7 units up.
