To find the image of the point $(-7, 4)$ after a $90^\circ$ counterclockwise rotation about the origin, we use the rotation transformation rule for $90^\circ$ counterclockwise:

$(x, y) \rightarrow (-y, x)$

For the point $(-7, 4)$:

• $x = -7$
• $y = 4$

Applying the transformation: $(-7, 4) \rightarrow (-4, -7)$

The image of the point $(-7, 4)$ after a $90^\circ$ counterclockwise rotation about the origin is:

$(-4, -7)$

Would you like further details or a graphical explanation?

---

Related Questions:

1. What is the result of a $180^\circ$ rotation for the same point?
2. How would a $90^\circ$ clockwise rotation change the coordinates?
3. Can you generalize the rule for a $270^\circ$ counterclockwise rotation?
4. What would the coordinates be if reflected across the x-axis instead of rotated?
5. How does the transformation change if the center of rotation is not the origin?

Tip:

Always visualize rotations with reference to quadrants to avoid errors.