To understand the translation described by the rule [tex]\((x, y) \rightarrow (x-2, y+7)\)[/tex], let’s break down the transformations applied to the coordinates [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
1. Translation in the [tex]\(x\)[/tex]-direction:
- The original coordinate [tex]\(x\)[/tex] becomes [tex]\(x-2\)[/tex].
- Subtracting 2 from the [tex]\(x\)[/tex]-coordinate means that each point is moved 2 units to the left.
2. Translation in the [tex]\(y\)[/tex]-direction:
- The original coordinate [tex]\(y\)[/tex] becomes [tex]\(y+7\)[/tex].
- Adding 7 to the [tex]\(y\)[/tex]-coordinate means that each point is moved 7 units up.
Combining these two transformations, the rule [tex]\((x, y) \rightarrow (x-2, y+7)\)[/tex] describes:
- A translation of 2 units to the left and
- A translation of 7 units up.
Therefore, the correct option is:
- a translation of 2 units to the left and 7 units up.
The correct description of this translation is:
a translation of 2 units to the left and 7 units up.
