Rotate a point on a line at (−4, 6) 180° counterclockwise. What is the resulting point?

Question

1. (−6, 4)
2. (6, −4)
3. (-4, −6)
4. (4, −6)

Answer 1

To rotate a point \((x, y)\) 180° counterclockwise around the origin, you can use the transformation:

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

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

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

So the resulting point after rotating \((-4, 6)\) 180° counterclockwise is \((4, -6)\).

Thus, the answer is \(4. \ (4, -6)\).