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).

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!