Given a point on a geometric figure (x, y)

Question

, 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 think of it as rotating the point $90$ degrees counterclockwise.

The formula for rotating a point $(x,y)$ counterclockwise by $90$ degrees is: $$(x^{\prime },y^{\prime })=(-y,x)$$

So, for clockwise rotation by $270$ degrees, the new coordinates $(x^{\prime },y^{\prime })$ will be: $$(x^{\prime },y^{\prime })=(-y,x)$$

Thus, the new point after a $270$ degree clockwise rotation about the origin is $(-y,x)$.