Question

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?

Answer 1

To rotate a point \((x, y)\) clockwise about the origin by 270 degrees, you can use the rotation formula for clockwise rotations. A clockwise rotation by 270 degrees is equivalent to a counterclockwise rotation by 90 degrees.

The rotation formulas for a point \((x, y)\) when rotated counterclockwise by 90 degrees are:
\[
(x', y') = (-y, x)
\]

Thus, if you are rotating clockwise by 270 degrees, the new coordinates will be:
\[
(x', y') = (-y, x)
\]

So, given a point \((x, y)\), the new point after rotating 270 degrees clockwise about the origin is:
\[
(-y, x)
\]