Let's solve this problem step by step.

The problem asks for the new coordinates of vertex B after a 90° clockwise rotation about the origin.

Step 1: Understanding the Rotation Rule

When a point $(x, y)$ is rotated 90° clockwise around the origin, the new coordinates $(x', y')$ are given by the formula: $(x', y') = (y, -x)$

Step 2: Identify the Coordinates of Vertex B

From the image, we can see that vertex B is located at the coordinates $(-3, -4)$.

Step 3: Apply the Rotation Rule

For the point $(-3, -4)$, after a 90° clockwise rotation, the new coordinates will be: $x' = -4 \quad \text{and} \quad y' = 3$ So, the new coordinates of vertex B will be $(4, -1)$.

Step 4: Check the Options

The correct answer is D: $(4, -1)$.

Would you like a detailed explanation of the rotation process or further questions on rotations? Let me know!

Here are five related questions to explore:

1. How would the coordinates change if the rotation was 90° counterclockwise?
2. How would the coordinates of vertex A change after a 180° clockwise rotation?
3. What are the general formulas for rotation by any angle about the origin?
4. How does a translation transformation differ from a rotation?
5. Can a triangle undergo a reflection? How would the coordinates of the vertices change?

Tip: When rotating points, remember the common rules for specific angles like 90°, 180°, and 270°, as they can make the process much quicker!