Question

A ferris wheel is drawn on a coordinate plane so that the first car is located at the point ​(0​,40​). What are the coordinates of the first car after a rotation of 270 degrees° counterclockwise about the​ origin?

Answer 1

After a 270-degree counterclockwise rotation, the first car on the ferris wheel originally located at (0, 40) will be at (40, 0).

Step-by-step explanation:

If the first car of a ferris wheel is located at the point (0, 40) on a coordinate plane and undergoes a rotation of 270 degrees counterclockwise about the origin, the new coordinates of the first car can be determined by applying a rotation transformation. To perform a 270-degree counterclockwise rotation, we rotate the point 90 degrees clockwise. This equivalent action simplifies the calculation, as rotating (0, 40) 90 degrees clockwise results in the point moving to (40, 0). Therefore, after a 270-degree counterclockwise rotation (which is equivalent to a 90-degree clockwise rotation), the new coordinates of the first car on the ferris wheel are (40, 0).

Answer 2

(40,0)

Step-by-step explanation:

A rotation of 270 degrees° counterclockwise about the​ origin has the rule

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

A ferris wheel is drawn on a coordinate plane so that the first car is located at the point ​(0​,40​).

According to the given rule, the image point after a rotation of 270 degrees° counterclockwise about the​ origin have the coordinates (40,0) (see attached diagram for details).