Given a point (x, y)

on a geometric figure, what is the new point when the figure is rotated counterclockwise about the origin 180 degrees?

1 answer

When a point \((x, y)\) is rotated counterclockwise about the origin by 180 degrees, the new coordinates can be determined by using the following transformation:

\[ (x', y') = (-x, -y) \]

This means that the \(x\) coordinate becomes its negative, and the \(y\) coordinate also becomes its negative.

So, if you start with a point \((x, y)\), after a 180-degree counterclockwise rotation about the origin, the new point will be \((-x, -y)\).