A car ride is drawn on a coordinate plane so that the first card is located at the point by (5,10) what are the coordinates of the first car after a rotation of 270° about the origin

There are two possible solutions:

Clockwise rotation

Counterclockwise rotation

Step-by-step explanation:

There are two possible answers: (i) Clockwise rotation, (ii) Counterclockwise rotation. Vectorially speaking, rotation of point of rotation of a point about another point of reference is defined by:

(1)

Where:

- Point of reference.

- Length of the segment OP.

- Direction of segment OP, measured in sexagesimal degrees.

- Angle of rotation, measured in sexagesimal degrees.

Please notice that clockiwise rotation occurs when and counterclockwise rotation when . In addition, we define length and direction of the segment below:

(1)

If we know that , , and , then the coordinates of the first car after rotation is:

Please notice that original point is located at first quadrant of the Cartesian plane centered at origin, then the direction of the segment OP is:

The two solutions are finally presented:

Clockwise rotation

Counterclockwise rotation