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Rotate the point (-4,6) on a geometric figure 180 degrees counterclockwise. What is the new point? point

(6, 4)
(4,6)
(-4, 6)
(-6,-4)

1 answer

To rotate a point 180 degrees counterclockwise around the origin, you can use the transformation rule:

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

For the point (-4, 6):

  1. Take the x-coordinate: -4 becomes 4.
  2. Take the y-coordinate: 6 becomes -6.

So, after rotating (-4, 6) 180 degrees counterclockwise, the new point is (4, -6).

However, let's examine the options you provided:

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

None of these points matches (4, -6). It appears there is no correct option listed in your choices based on the 180-degree rotation calculation provided. The result of rotating the point (-4, 6) 180 degrees counterclockwise is (4, -6).