Given a point (-6, 4) in a line segment, what is the new point when the line segment is rotated counterclockwise about the origin 180 degrees?
To rotate a point counterclockwise about the origin, we can use the following rotation formula:
(x', y') = (x*cos(θ) - y*sin(θ), x*sin(θ) + y*cos(θ))
In this case, the point (-6, 4) is rotated 180 degrees counterclockwise about the origin, so θ = 180 degrees.
Substituting the values in the formula, we get:
(x', y') = (-6*cos(180) - 4*sin(180), -6*sin(180) + 4*cos(180))
The cosine of 180 degrees is -1, and the sine of 180 degrees is 0:
(x', y') = (-6*(-1) - 4*0, -6*0 + 4*(-1))
(x', y') = (6, -4)
Therefore, when the line segment is rotated counterclockwise about the origin 180 degrees, the new point is (6, -4).