To find the image of the point (1, 6) after a 90-degree counterclockwise rotation about the origin, we can use the rotation formula for points in the Cartesian plane.
The formula for rotating a point (x, y) counterclockwise by an angle θ is:
(x’, y’) = (x * cos(θ) – y * sin(θ), x * sin(θ) + y * cos(θ))
For a 90-degree rotation, θ = 90 degrees. Therefore:
- cos(90°) = 0
- sin(90°) = 1
Now, substituting the values into the formula:
- x’ = 1 * 0 – 6 * 1 = 0 – 6 = -6
- y’ = 1 * 1 + 6 * 0 = 1 + 0 = 1
Thus, the image of the point (1, 6) after a 90-degree counterclockwise rotation about the origin is (-6, 1).