https://file.aiquickdraw.com/mathbot/file/1726152462443j1kab2i9.jpg

The image displays a line segment on a coordinate plane, with points \(A\) and \(B\) clearly marked. The question asks to find the new coordinates of point \(B\) after the line segment is translated **down by 4 units**.

Let's analyze the steps:

1. First, we need to determine the original coordinates of point \(B\) on the graph. From observation, the coordinates of \(B\) are \((4, 3)\).

2. Since the line segment is translated **down by 4 units**, we subtract 4 from the y-coordinate of point \(B\):
   \[
   (x', y') = (x, y - 4)
   \]
   Applying this to point \(B\)'s original coordinates:
   \[
   B'(4, 3 - 4) = (4, -1)
   \]

Thus, the new coordinates of point \(B\) after the translation are \(\boxed{(4, -1)}\), which corresponds to option **D**.

Would you like further details or have any questions?

Here are some related questions:
1. How do translations affect the equation of a line?
2. What are the coordinates of point \(A\) after the same translation?
3. How do translations differ from other transformations like rotations or reflections?
4. Can you translate a line by a combination of both horizontal and vertical shifts?
5. What happens to the slope of the line after the translation?

**Tip:** When translating a point, you only change its position without affecting the shape or orientation of any geometric figure.

The line segment shown is translated down 4 units, what are the new coordinates of B?

Find the new coordinates of point B after translating the line segment down by 4 units. This problem involves understanding how translations affect points on a coordinate plane, and applying the translation formula to adjust the y-coordinate.

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