To rotate coordinates by 90 degrees counterclockwise, you can use the following transformation matrix:

2D Rotation Formula:

If a point has coordinates $(x, y)$, after rotating it 90 degrees counterclockwise, the new coordinates $(x', y')$ are given by:

$x' = -y$ $y' = x$

This is derived from the 2D rotation matrix:

x' \\ y' \end{bmatrix} = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}$$ ### Explanation: - The new x-coordinate becomes the negative of the original y-coordinate. - The new y-coordinate becomes the original x-coordinate. If you want to rotate clockwise instead, you would use the inverse transformation: $$x' = y$$ $$y' = -x$$ Would you like an example of how to apply this to specific points, or more details on rotation in other dimensions? --- ### 5 Related Questions: 1. How do I rotate a point 180 degrees in 2D space? 2. Can the rotation formula be used for 3D coordinates as well? 3. What happens to the coordinates when rotating by 270 degrees counterclockwise? 4. How can I apply these formulas in a programming language like Python? 5. What is the relationship between rotation matrices and transformation matrices? ### Tip: When performing a coordinate rotation, remember that the rotation angle is always measured counterclockwise from the positive x-axis.