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) about the origin 270 degrees clockwise, you can use the following formulas:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
where theta represents the angle of rotation.
For a clockwise rotation of 270 degrees (or 3/4 of a full rotation), the value of theta would be -3π/2 (since 270 degrees = -3π/2 radians).
Substituting the values into the formulas:
x' = x * cos(-3π/2) - y * sin(-3π/2)
y' = x * sin(-3π/2) + y * cos(-3π/2)
Simplifying further:
x' = -y
y' = x
Therefore, the new point obtained by rotating a point (x, y) 270 degrees clockwise about the origin would be (-y, x).