To determine the translation described by the mapping rule [tex]\((x, y) \rightarrow (x-2, y+7)\)[/tex], we need to analyze how the coordinates of the points change:
1. Horizontal Translation ([tex]\(x-2\)[/tex]):
- The [tex]\(x\)[/tex]-coordinate is reduced by 2 units. This means that every point on the rectangle moves 2 units to the left.
2. Vertical Translation ([tex]\(y+7\)[/tex]):
- The [tex]\(y\)[/tex]-coordinate is increased by 7 units. This means that every point on the rectangle moves 7 units up.
Now, we summarize the two components of the translation:
- Moving 2 units to the left (because [tex]\(x-2\)[/tex]).
- Moving 7 units up (because [tex]\(y+7\)[/tex]).
Putting these together, the entire translation described by the rule [tex]\((x, y) \rightarrow (x-2, y+7)\)[/tex] is a translation of 2 units to the left and 7 units up.
Therefore, the correct option is:
- a translation of 2 units to the left and 7 units up.
