what is the rule for rotating 90 degrees counterclockwise

To rotate a point 90 degrees counterclockwise about the origin, you use this rule:

(x,y)→(−y,x)(x,y)\rightarrow (-y,x)(x,y)→(−y,x)

Quick Scoop: The Core Rule

• Start with a point (x,y)(x,y)(x,y).
• After a 90° counterclockwise rotation about the origin, its new coordinates become (−y,x)(-y,x)(−y,x).

So for example:

• (3,2)(3,2)(3,2) → (−2,3)(-2,3)(−2,3).

• (−4,1)(−4,1)(−4,1) → (−1,−4)(−1,−4)(−1,−4).

Why This Works (Short Version)

A 90° counterclockwise turn:

• Moves every point a quarter-turn around the origin.
• Swaps the roles of xxx and yyy, then makes the original yyy negative, giving (−y,x)(-y,x)(−y,x).

You can think of it as:

• Slide the y-value into the x-spot and negate it.
• Slide the x-value into the y-spot unchanged.

Mini Checklist to Use the Rule

1. Take your original point (x,y)(x,y)(x,y).
2. Write the new point as (−y,x)(-y,x)(−y,x).
3. Plot the new point to see the rotated position.

If you’re working with a whole shape, just apply (x,y)→(−y,x)(x,y)\rightarrow (-y,x)(x,y)→(−y,x) to every vertex.

TL;DR:
The rule for rotating 90 degrees counterclockwise about the origin is: (x,y)→(−y,x)(x,y)\rightarrow (-y,x)(x,y)→(−y,x).

Information gathered from public forums or data available on the internet and portrayed here.