Given a point (x,y) which is the new point when the point is rotated counterclockwise about the origin 270 degrees

Answer 1

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

x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)

In this case, we want to rotate the point (x, y) by 270 degrees counterclockwise, so theta = 270 degrees. Converting 270 degrees to radians, we get theta = 3π/2.

Substituting the values into the rotation formula:

x' = x * cos(3π/2) - y * sin(3π/2)
y' = x * sin(3π/2) + y * cos(3π/2)

Now, we can simplify these equations:

x' = x * 0 - y * (-1) = y
y' = x * (-1) + y * 0 = -x

Therefore, the new point (x', y') when the point (x, y) is rotated counterclockwise about the origin by 270 degrees is (y, -x).