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 use the following transformation:

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

For the point \((-6, 4)\):

1. Apply the transformation:
   • \(x = -6\) becomes \( -(-6) = 6\)
   • \(y = 4\) becomes \(-4\)

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

\[ (6, -4) \]