Answer:
a)(x,y)→ (-y, x)
Step-by-step explanation:
The answer is (a) (x, y) → (-y, x).
Here's why:
Counterclockwise Rotation: A 90-degree counterclockwise rotation means turning a point 90 degrees to the left around the origin.
Switching Coordinates: This rotation involves swapping the x and y coordinates, but also negating the new x-coordinate (which becomes the original y-coordinate).
Visualizing:
Imagine a point at (2, 3). Rotating it 90 degrees counterclockwise moves it to (-3, 2). The x-coordinate becomes -3, and the y-coordinate becomes 2.
Understanding the Other Options:
(b) (x, y) → (y, -x): This rule represents a 90-degree clockwise rotation.
(c) (x, y) → (-x, -y): This rule represents a 180-degree rotation (flipping the point across the origin).
(d) (x, y) → (x, -y): This rule reflects the point across the x-axis, not rotating it.
