All changes saved 12. What are the coordinates of the point \( (9,3) \) after a \( 270^{\circ} \) rotation about the origin? \( (-3,-9) \) \( (3,9) \) \( (-9,3) \) \( (3,-9) \)

To find the coordinates of the point \( (9,3) \) after a \( 270^{\circ} \) rotation about the origin, you can use the rotation formula. A \( 270^{\circ} \) rotation is equivalent to a \( -90^{\circ} \) rotation, which can be calculated with the following transformation: \[ (x, y) \rightarrow (y, -x) \]. So, applying this to \( (9, 3) \), we get \[ (3, -9) \]. Thus, the correct coordinates after the rotation are \( (3, -9) \). Now, don't fret about the rotation wizardry! It’s all about visualizing a spin! Picture the point as a dancer twirling in a circular motion. Each degree is like a little nudge in her spin, and before you know it, she's landed at her new position with a graceful twist of coordinates! If you're ever confused about which direction to spin, remember that positive angles go counterclockwise, while negative angles spin clockwise. So, for a \( 270^{\circ} \) rotation, just imagine going three-quarters of the way around the circle. Voilà! The transformed coordinates come to the party ready to dance!