Question

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

Answer 1

When a point is rotated counterclockwise about the origin, the new point can be found by applying the following transformation:

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

Where (x', y') is the new point, (x, y) is the original point, and a is the angle of rotation in radians.

In this case, the angle of rotation is 270 degrees, which is equivalent to 3/2 * π radians.

Let's use this formula to find the new point:
x' = x * cos(3/2 * π) - y * sin(3/2 * π)
y' = x * sin(3/2 * π) + y * cos(3/2 * π)

Since cos(3/2 * π) = 0 and sin(3/2 * π) = -1, the formulas become:
x' = -y
y' = x

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