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
To rotate a point (x, y) clockwise about the origin by 270 degrees, we can use the following formulas:
x' = x * cos(θ) + y * sin(θ)
y' = -x * sin(θ) + y * cos(θ)
Here, θ is the angle of rotation, which in this case is 270 degrees.
Substituting the values:
θ = 270 degrees
cos(θ) = cos(270 degrees) = 0
sin(θ) = sin(270 degrees) = -1
We can calculate the new coordinates as follows:
x' = x * cos(θ) + y * sin(θ)
= x * 0 + y * (-1)
= -y
y' = -x * sin(θ) + y * cos(θ)
= -x * (-1) + y * 0
= x
Therefore, the new point after rotating (x, y) by 270 degrees clockwise about the origin is (-y, x).