https://file.aiquickdraw.com/mathbot/file/1729822023633io7t9exz.jpg

The problem in the image asks to find the new coordinates of point \( A(1, 5) \), which is translated successively by the vectors:

\[
\begin{pmatrix} -4 \\ 3 \end{pmatrix} \quad \text{and} \quad \begin{pmatrix} 6 \\ -1 \end{pmatrix}.
\]

### Step-by-step Solution:

1. **First translation** by the vector \(\begin{pmatrix} -4 \\ 3 \end{pmatrix}\):
   \[
   A(1, 5) \rightarrow A_1(x_1, y_1)
   \]
   \[
   x_1 = 1 + (-4) = -3 \quad \text{and} \quad y_1 = 5 + 3 = 8
   \]
   So, after the first translation, the new point is \( A_1(-3, 8) \).

2. **Second translation** by the vector \(\begin{pmatrix} 6 \\ -1 \end{pmatrix}\):
   \[
   A_1(-3, 8) \rightarrow A'(x', y')
   \]
   \[
   x' = -3 + 6 = 3 \quad \text{and} \quad y' = 8 + (-1) = 7
   \]
   So, after the second translation, the final point is \( A'(3, 7) \).

Thus, the correct answer is **(b) A'(3, 7)**.

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Would you like more details or explanations on any step?

Here are 5 related questions to explore this concept further:
1. What is the general formula for translating a point by a vector?
2. How do multiple translations affect the final position of a point?
3. What is the difference between translating and rotating a point?
4. How would you apply this method in three-dimensional space?
5. Can translations be expressed as matrix multiplications?

**Tip:** Always apply each translation vector independently to avoid calculation errors when translating points multiple times.

Titik A(1, 5) ditranslasikan berturut-turut oleh [ -4 3 ] dan [ 6 -1 ]. Koordinat bayangan titik A adalah?

Learn how to translate the point A(1, 5) successively by vectors [-4, 3] and [6, -1]. Follow a detailed step-by-step solution to find the final coordinates after both translations. Suitable for students in Grades 9-10 studying coordinate geometry.

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