Question

A ferris wheel is drawn on a coordinate plane so that the first car is located at the point (10,0) What are the coordinates of the first car after a rotation of 270 counterclockwise about the origin?

Answer 1

After a 270-degree counterclockwise rotation about the origin, the Ferris wheel car which started at (10,0) will be located at (0,-10).

Step-by-step explanation:

To determine the coordinates of the first car on a Ferris wheel after a rotation of 270 degrees counterclockwise about the origin, we apply the rules of rotation on the coordinate plane. The original coordinates of the first car are at the point (10,0). A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.

When we rotate a point 90 degrees clockwise about the origin, the new x-coordinate becomes the original y-coordinate, and the new y-coordinate becomes the negative of the original x-coordinate. Thus, after the rotation, the new coordinates will be (0, -10).