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 by 180 degrees, we can multiply the coordinates of the point by the rotation matrix:
| cos θ -sin θ |
| sin θ cos θ |
where θ is the angle of rotation in radians.
For a 180 degree rotation, this becomes:
| -1 0 |
| 0 -1 |
Multiplying the coordinates of the point (-6, 4) by this matrix, we get:
| -1 0 | | -6 | | -1*(-6) + 0*4 | | 6 |
| 0 -1 | * | 4 | = | 0*(-6) + (-1)*4 | = | -4 |
Therefore, the new point when the line segment (-6, 4) is rotated counterclockwise about the origin 180 degrees is (6, -4).