Given a point (−6, 4)

Question

in a line segment, what is the new point when the line segment is rotated counterclockwise about the origin 180 degrees

Answer 1

To rotate a point \((x, y)\) counterclockwise about the origin by 180 degrees, you can use the following transformation:

\[ (x, y) \rightarrow (-x, -y) \]

For the point \((-6, 4)\), we apply this transformation:

\[ (-6, 4) \rightarrow (6, -4) \]

Therefore, after rotating the point \((-6, 4)\) counterclockwise about the origin by 180 degrees, the new point is \((6, -4)\).