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The problem involves translating and reflecting a point geometrically.

1. The point B has coordinates (3,2).
2. It is translated using the vector \( T = \begin{bmatrix} 3 \\ 1 \end{bmatrix} \).
3. Then it is reflected across the vertical line \( x = 4 \).

### Step 1: Translation
To translate the point \( B(3,2) \) by the vector \( T = \begin{bmatrix} 3 \\ 1 \end{bmatrix} \):
- New \( x \)-coordinate: \( 3 + 3 = 6 \)
- New \( y \)-coordinate: \( 2 + 1 = 3 \)

After translation, the new point is \( B'(6, 3) \).

### Step 2: Reflection across \( x = 4 \)
To reflect the point \( B'(6, 3) \) across the line \( x = 4 \), we calculate the horizontal distance from the point to the line:
- Distance from \( 6 \) to \( 4 \) is \( 6 - 4 = 2 \).
- To reflect, we subtract this distance from \( 4 \), which gives \( 4 - 2 = 2 \).

The \( y \)-coordinate remains the same during a reflection across a vertical line.

Thus, the final reflected point is \( B''(2, 3) \).

### Conclusion
None of the provided answers matches \( B''(2, 3) \), which indicates a discrepancy with the given options. Would you like to further analyze this or explore related concepts?

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Here are 5 related questions to expand your understanding:
1. What is the general formula for translating a point by a vector?
2. How do you reflect a point across a vertical line?
3. Can you explain how translation affects the geometry of shapes?
4. How would the reflection change if we reflected across the line \( y = 4 \) instead?
5. What are some real-world applications of point reflection and translation?

**Tip:** When reflecting a point across a vertical line, the \( y \)-coordinate stays the same while the \( x \)-coordinate changes symmetrically.

Titik B (3,2) ditranslasikan dengan T = [3,1] dan di refleksikan terhadap garis x = 4, maka bayangan titik B adalah ....

Solve a coordinate geometry problem where a point B(3,2) is translated by T = [3,1] and reflected across the line x = 4. Learn the step-by-step process of translating and reflecting points with detailed solutions. Suitable for Grades 9-12.

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