To rotate counterclockwise, you move a point or object around a fixed center point in the opposite direction that the hands of a clock move.
Think of it like this:
- Clockwise: The direction the hands on a clock move.
- Counterclockwise (or Anticlockwise): The opposite direction the hands on a clock move.
Rotation Rules in the Coordinate Plane:
In a coordinate plane, rotating a point counterclockwise around the origin (0, 0) follows specific rules depending on the degree of rotation:
- 90° Counterclockwise: (x, y) becomes (-y, x) - You negate the original y-coordinate and then swap the x and y values.
- 180° Counterclockwise: (x, y) becomes (-x, -y) - You negate both the x and y coordinates.
- 270° Counterclockwise: (x, y) becomes (y, -x) - You negate the original x-coordinate and then swap the x and y values.
Example:
Let's say we have the point (2, 3).
- Rotating (2, 3) 90° counterclockwise results in (-3, 2).
- Rotating (2, 3) 180° counterclockwise results in (-2, -3).
- Rotating (2, 3) 270° counterclockwise results in (3, -2).
- Rotating (2, 3) 360° counterclockwise results in (2, 3) - A full rotation returns the point to its original position.
In essence, rotating counterclockwise involves moving in the opposite direction of a clock's hands, and in the coordinate plane, specific rules govern how the coordinates of a point change based on the degree of rotation.
