Given a point (x, y), what is the new point when the point is rotated counterclockwise about the origin 270 degrees?
The new point when the point (x, y) is rotated counterclockwise about the origin 270 degrees is (-y, x).
To rotate a point counterclockwise about the origin, we can use the following formulas:
New x-coordinate = old x-coordinate * cos(angle) - old y-coordinate * sin(angle)
New y-coordinate = old x-coordinate * sin(angle) + old y-coordinate * cos(angle)
In this case, the angle of rotation is 270 degrees.
Let's calculate the new coordinates:
New x-coordinate = x * cos(270°) - y * sin(270°)
New y-coordinate = x * sin(270°) + y * cos(270°)
Now, let's evaluate these formulas:
New x-coordinate = x * cos(270°) - y * sin(270°)
= x * (0) - y * (-1)
= -y
New y-coordinate = x * sin(270°) + y * cos(270°)
= x * (-1) + y * (0)
= -x
Therefore, the new point (x', y') after rotating the point (x, y) counterclockwise about the origin by 270 degrees is (-y, -x).