To rotate the point $(4, 3)$ clockwise by $270^\circ$, you can follow these steps:

1. A $270^\circ$ clockwise rotation is equivalent to a $90^\circ$ counterclockwise rotation.
2. The rule for a $90^\circ$ counterclockwise rotation of a point $(x, y)$ is:
   $(x, y) \rightarrow (-y, x)$.
3. Applying this to $(4, 3)$:
   $(4, 3) \rightarrow (-3, 4)$.

Thus, the new coordinates after the rotation are $(-3, 4)$.

Would you like more details or have any questions about the process?

Here are five related questions to expand on this:

1. How do you rotate points by other angles like $180^\circ$?
2. What is the rule for rotating points counterclockwise by $270^\circ$?
3. How do you apply rotation transformations using matrices?
4. What happens when you rotate the same point multiple times?
5. How would you graphically verify this rotation on a coordinate plane?

Tip: When rotating points, always remember the signs of the coordinates will change depending on the direction and angle of rotation.