To understand the geometrical effect of the translation rule given as [tex]\((x, y) \rightarrow (x-2, y+7)\)[/tex], let's break down the components individually:
1. The [tex]\( x \)[/tex]-coordinate transformation:
- The rule states [tex]\( x \rightarrow x - 2 \)[/tex].
- This means that for any point on the rectangle, its [tex]\( x \)[/tex]-coordinate will be modified by subtracting 2 units.
- Subtracting 2 from the [tex]\( x \)[/tex]-coordinate shifts the point 2 units to the left.
2. The [tex]\( y \)[/tex]-coordinate transformation:
- The rule states [tex]\( y \rightarrow y + 7 \)[/tex].
- This means that for any point on the rectangle, its [tex]\( y \)[/tex]-coordinate will be modified by adding 7 units.
- Adding 7 to the [tex]\( y \)[/tex]-coordinate shifts the point 7 units upward.
By combining these two changes, the translation moves each point of the rectangle 2 units to the left and 7 units up.
Thus, the description that fits this translation is:
- "a translation of 2 units to the left and 7 units up".
Therefore, the correct answer is:
a translation of 2 units to the left and 7 units up.
