To determine which description accurately represents the given translation rule [tex]\((x, y) \rightarrow (x-2, y+7)\)[/tex], we need to analyze how the coordinates of any point [tex]\((x, y)\)[/tex] change according to this rule.
1. The new [tex]\(x\)[/tex]-coordinate is obtained by subtracting 2 from the original [tex]\(x\)[/tex]-coordinate: [tex]\(x-2\)[/tex]. This tells us that each point moves 2 units to the left along the [tex]\(x\)[/tex]-axis.
2. The new [tex]\(y\)[/tex]-coordinate is obtained by adding 7 to the original [tex]\(y\)[/tex]-coordinate: [tex]\(y+7\)[/tex]. This tells us that each point moves 7 units up along the [tex]\(y\)[/tex]-axis.
Putting these two observations together, the description that fits this translation rule is:
- A translation of 2 units to the left and 7 units up.
So the correct answer is:
a translation of 2 units to the left and 7 units up.
