Final Answer:
If the original coordinates of point Q are (x, y), after a 90-degree counterclockwise rotation about the origin, the new coordinates Q' are (-y, x).
Step-by-step explanation:
To rotate a point 90 degrees counterclockwise about the origin, a simple geometric transformation can be applied. Consider a point Q with coordinates (x, y). After the rotation, the x-coordinate of Q' becomes -y, and the y-coordinate becomes x. This transformation can be understood by visualizing the rotation of the point in a coordinate plane.
When a point is rotated counterclockwise by 90 degrees about the origin, it essentially moves to a new position such that the original x-coordinate becomes the negative of the original y-coordinate, and the original y-coordinate becomes the original x-coordinate. This transformation preserves the distance of the point from the origin but changes its direction in the plane. The negative sign for the x-coordinate ensures the counterclockwise rotation, while swapping x and y captures the essence of the 90-degree transformation.
In summary, the coordinates of the image point Q' after a 90-degree counterclockwise rotation about the origin are given by (-y, x), providing a concise and straightforward representation of the geometric transformation.