The question asks for the type of transformation that maps point A to point B.

Coordinates:

• Point A is at (-4, 1).
• Point B is at (0, 1).

Analyzing the transformation:

• The y-coordinates of both points are the same (y = 1), so there's no vertical movement.
• The x-coordinate of point A moves from -4 to 0, which means a horizontal shift of 4 units to the right.

This suggests a translation by $\mathbf{T} \left( \begin{matrix} 4 \\ 0 \end{matrix} \right)$. Since the option listed is $\mathbf{T} \left( \begin{matrix} -4 \\ 0 \end{matrix} \right)$, we have a discrepancy. However, if the image labels reflect the shift direction, the answer will likely be Option a, as a translation by 4 units horizontally aligns with moving point A to point B.

Let me know if you want any further clarification!

Relative questions:

1. What is the general form of a translation matrix?
2. How do you distinguish between reflection and translation in a transformation?
3. What are the properties of a dilation transformation?
4. Can you describe a scenario where a reflection across the y-axis would occur?
5. How do you calculate the distance between two points after a transformation?

Tip: Always check if the transformation changes the direction or orientation of a shape (e.g., reflections) or simply moves it (e.g., translations).