To find the image of the point \( U(7, 9) \) after a rotation of 90° counterclockwise around the origin, you can use the following transformation for coordinates when rotating counterclockwise:
\[ (x, y) \rightarrow (-y, x) \]
Here, \( (x, y) \) are the original coordinates of the point.
For the point \( U(7, 9) \):
- \( x = 7 \)
- \( y = 9 \)
Applying the transformation for a 90° counterclockwise rotation, we get:
\[ (7, 9) \rightarrow (-9, 7) \]
Therefore, the image of the point \( U(7, 9) \) after a 90° counterclockwise rotation around the origin is \( U'(-9, 7) \).
To graph the rotation:
- Start with the point \( U(7, 9) \).
- Plot the new point \( U'(-9, 7) \) on the coordinate plane.
This will give you a visual representation of the rotation.