Given a point on a geometric figure (x, y), what is the new point when the figure is rotated clockwise about the origin 270 degrees?
When a point is rotated clockwise about the origin, the new coordinates are given by:
New x-coordinate = x * cos(θ) + y * sin(θ)
New y-coordinate = -x * sin(θ) + y * cos(θ)
In this case, since the figure is being rotated 270 degrees clockwise, θ = 270°.
So, the new x-coordinate = x * cos(270°) + y * sin(270°)
= x * 0 + y * (-1)
= -y
And the new y-coordinate = -x * sin(270°) + y * cos(270°)
= -x * (-1) + y * 0
= x
Hence, the new point is (-y, x).