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 (x, y) is rotated clockwise about the origin by an angle of 270 degrees, the new point (x', y') can be found using the following formulas:
x' = x * cos(270°) - y * sin(270°)
y' = x * sin(270°) + y * cos(270°)
For a rotation of 270 degrees, we have:
x' = x * cos(270°) - y * sin(270°)
= x * cos(-90°) - y * sin(-90°)
= x * cos(90°) + y * sin(90°)
= -y
y' = x * sin(270°) + y * cos(270°)
= x * sin(-90°) + y * cos(-90°)
= x * sin(90°) - y * cos(90°)
= x
Therefore, the new point after rotating (x, y) clockwise about the origin by 270 degrees is (-y, x).