Question

What is the image of point (4, 5) after a counterclockwise rotation of 270º about the origin?

Answer 1

A counterclockwise rotation of 270º about the origin is equivalent to a clockwise rotation of 90º about the origin.

Given a point (4, 5), the x-value, i.e. 4 and the y-value, i.e. 5 are positive, hence the point is in the 1st quadrant of the xy-plane.

A clockwise rotation of 90º about the origin of a point in the first quadrant of the xy-plane will have its image in the fourth quadrant of the xy-plane. Thus the x-value of the image remains positive but the y-value of the image changes to negative.
Also the x-value and the y-value of the original figure is interchanged.
For example, given a point (a, b) in the first quadrant of the xy-plane, a counterclockwise rotation of 270º about the origin which is equivalent to a clockwise rotation of 90º about the origin will result in an image with the coordinate of (b, -a)

Therefore, a counterclockwise rotation of 270º about the origin of the point (4, 5) will result in an image with the coordinate of (5, -4) (option C)