Given a point x, y what is the new point when the point is rotated counterclockwise about the origin 270°

Answer 1

To rotate a point counterclockwise about the origin, we can use the following formulas:

NewX = x * cos(angle) - y * sin(angle)
NewY = x * sin(angle) + y * cos(angle)

In this case, the angle of rotation is 270°.
Converting 270° to radians:
270° * (π/180°) = (3π/2)

Using the formulas:

NewX = x * cos(3π/2) - y * sin(3π/2)
= x * 0 - y * (-1)
= y

NewY = x * sin(3π/2) + y * cos(3π/2)
= x * (-1) + y * 0
= -x

Therefore, the new coordinates after rotating the point (x, y) counterclockwise about the origin 270° are (y, -x).