To find the result of translating the point [tex]\((9, -5)\)[/tex] using the rule [tex]\((x, y) \rightarrow (x+7, y-2)\)[/tex], follow these steps:
1. Identify the initial point coordinates:
The initial coordinates are [tex]\((x, y) = (9, -5)\)[/tex].
2. Apply the translation rule to the [tex]\(x\)[/tex]-coordinate:
According to the rule, the new [tex]\(x\)[/tex]-coordinate is calculated as:
[tex]\[
x + 7 = 9 + 7 = 16
\][/tex]
3. Apply the translation rule to the [tex]\(y\)[/tex]-coordinate:
According to the rule, the new [tex]\(y\)[/tex]-coordinate is calculated as:
[tex]\[
y - 2 = -5 - 2 = -7
\][/tex]
4. Combine the translated coordinates:
The new coordinates after the translation are [tex]\((16, -7)\)[/tex].
Therefore, the result of translating the point [tex]\((9, -5)\)[/tex] using the rule [tex]\((x, y) \rightarrow (x+7, y-2)\)[/tex] is [tex]\((16, -7)\)[/tex].
The correct answer is:
D) [tex]\((16, -7)\)[/tex].
