Given a point (x, y), what is the new point when the point is rotated counterclockwise about the origin 270 degrees?(1 point)
The new point when a point (x, y) is rotated counterclockwise about the origin 270 degrees can be found by applying the rotation matrix. The rotation matrix for a counterclockwise rotation of θ degrees is:
| cos(θ) -sin(θ) |
| sin(θ) cos(θ) |
In this case, θ is 270 degrees. So the rotation matrix becomes:
| cos(270°) -sin(270°) |
| sin(270°) cos(270°) |
Simplifying the values:
| 0 1 |
| -1 0 |
To find the new point, we multiply this rotation matrix by the original point (x, y) as a column vector:
| 0 1 | | x | | 0*x + 1*y |
| -1 0 | * | y | = |-1*x + 0*y |
Therefore, the new point when the point (x, y) is rotated counterclockwise about the origin 270 degrees is (-y, x).