https://file.aiquickdraw.com/mathbot/file/1729600869011kfxjexki.jpg

The text in the image appears to be written in Indonesian. Here's a translation and analysis of the problem:

**Original text:**
- Titik A'(-6, 12) adalah bayangan titik A oleh translasi \(\begin{pmatrix} 2 \\ 9 \end{pmatrix}\). Koordinat titik A adalah....

**Translation:**
- Point A'(-6, 12) is the image of point A under the translation \(\begin{pmatrix} 2 \\ 9 \end{pmatrix}\). The coordinates of point A are...

### Solution:
A translation of a point means shifting it by a certain vector. In this case, we know that:
- The translation vector is \(\begin{pmatrix} 2 \\ 9 \end{pmatrix}\).
- The translated point A' is (-6, 12).

To find the original coordinates of point A, we reverse the translation. This means subtracting the translation vector from point A':

\[
A(x, y) = A'(-6, 12) - \begin{pmatrix} 2 \\ 9 \end{pmatrix}
\]

\[
x = -6 - 2 = -8
\]
\[
y = 12 - 9 = 3
\]

Thus, the coordinates of point A are **(-8, 3)**.

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Would you like more details on how this was solved, or do you have any other questions?

Here are 5 related questions for further exploration:
1. What is a translation in geometry?
2. How would you reverse a translation in a 3D coordinate system?
3. What other transformations can be applied to a point besides translation?
4. If the translation vector was negative, how would the solution change?
5. How would you describe the relationship between A and A' geometrically?

**Tip:** When performing translations, always remember that you add the translation vector to the original point's coordinates, and subtract it to go in reverse!

Titik A'(-6, 12) adalah bayangan titik A oleh translasi (2, 9). Koordinat titik A adalah?

Solve the translation problem where point A'(-6, 12) is the image of point A under the translation vector (2, 9). Find the original coordinates of point A. This problem involves key geometry concepts and is suitable for students in Grades 7-9.

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