How do you rotate 270 degrees counterclockwise about the origin? What is the rule for rotating 270 degrees about the origin? 

1. Understanding Rotation: 

Rotating a point 270 degrees counterclockwise about the origin is equivalent to rotating it 90 degrees clockwise. 
2. Rule: 

The general rule for rotating a point \(( x, y) \) 270 degrees counterclockwise about the origin is: 
\[( x, y) \rightarrow ( y, - x) \]
3. Example: 

If you have a point \(( 3, 4) \): 
\[( 3, 4) \rightarrow ( 4, - 3) \] 4. Explanation: 

This transformation swaps the coordinates and changes the sign of the new x-coordinate, effectively rotating the point 270 degrees counterclockwise.

Supplemental Knowledge:

Rotating a point or a shape in the coordinate plane involves turning it around a fixed point, typically the origin (0,0). When rotating points counterclockwise, specific rules apply based on the angle of rotation.

Rule for Rotating 270 Degrees Counterclockwise About the Origin:

To rotate a point \(( x, y) \) 270 degrees counterclockwise about the origin, you can use the following transformation rule:

The coordinates of the point after rotation will be \(( y, - x) \).

This rule is derived from understanding how each quadrant shifts during a 270-degree rotation: 
1. A 90-degree counterclockwise rotation transforms \(( x, y) \) to \(( - y, x) \). 
2. A 180-degree counterclockwise rotation transforms \(( x, y) \) to \(( - x, - y) \). 
3. A 270-degree counterclockwise rotation (or equivalently a 90-degree clockwise rotation) transforms \(( x, y) \) to \(( y, - x) \).

Theory in Practice:

Understanding rotations is integral for many real-world applications. If you're designing an animation where a character must move smoothly from side to side, being familiar with rotational transformations allows you to accurately program their movements and produce smooth animations.

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