Determine a rotation matrix for rotation by an arbitrary angle  about a fixed point (r , r ) x y in homogeneous form. Use this matrix to rotate the square with vertices (0, 0), (1, 0), (1,1) and (0, 1) about the point (1, 1)

To determine a rotation matrix for rotation by an arbitrary angle θ about a fixed point (r, r) in homogeneous form, we can follow these steps. Let's denote the original coordinates as (x, y) and the rotated coordinates as (x', y').

1. Translate the fixed point (r, r) to the origin by applying a translation matrix T.

\[ T = \begin{bmatrix} 1 & 0 & -r \\ 0 & 1 & -r \\ 0 & 0 & 1 \end{bmatrix} \]

This matrix will move the point (r, _________ _________ ____ _____ __________ _________ ________ _________ _________.
__________ __________ ________ _________ ________.
____ __________ ____ _________ ____.
______ _____ ____ __________ ________.
____ _______ _____ _______ ___ ___ __________ _______ ___ _____.
________ ________ __________ ___ _____ ______ ________ __________ _________ _____.
__________ __________ __________ _________ ____ _______ _______ _______.
__________ __________ _________ _________ ________ ________ ________ __________ ___.
________ ________ _____ __________ _____ __________.
__________ _______ _____ __________ __________ ____ ________ ______ ______ __________ ________ ______.
_____ ______ ______ ______ _____ _______ ______ ______.
___ ____ ________ __________ ______ _____ ______ _________ _______ _________.
_________ ______ ___ ____ ______ _____ ____ ____ ___ __________ _______ _______.
________ __________ _______ ____ _______ ____ _________ ________.
__________ ________ _________ _________ ______.
_____ ________ _________ ______ _________ ___.
____ _______ ____ ____ ____ ___ _________ ______ ____ ________ ______ ______.
________ _______ _____ _________ ______ ____ ______ _______ ____ _____ _________ _________.
__________ ___ ___ _____ _______ __________ ________ ________ __________.
______ ____ _______ _________ _____ ___ ___.
________ ________ ______ ______ __________ ____ _________ __________ ___ ________ _______ _________.
__________ _____ _________ __________ ___ _______ _____ _______ ______ ___.
__________ _________ ________ _______ _________ __________ _______.
____ _________ ___ __________ ____ __________ __________ _________ ______ ______.
______ _________ _______ __________ ___ ________.
_______ _______ __________ _____ ________ ___ _______ ____ _____ ______.
___ _________ _____ ___ ________.
_________ ______ _______ _______ ______ _____ _________ _______.
______ _______ _______ _________ ______ _______ ___ _________ _________.
__________ ___ ______ ________ ___ _____ ___ _________ ________ _____ ________ ____.
_____ ______ ________ _________ ______ __________ ______ _________ __________ ______ __________.
__________ _____ _______ ________ __________.
___ ______ __________ ________ ______ _______ ________ ______ _______ _______ ________.
_________ ___ _____ ____ ____ ______ _______.
__________ ____ __________ ________ ________ ___ _________ ______ ______ ________ _______.
____ _____ ________ ______ __________.
__________ ____ ______ ____ _____ __________ _________.
_______ _________ ________ _____ _____ ______ ______ ____ ________ _____ _______.
______ _____ ___ ____ _______.
___ _______ ________ ______ __________ ______ ________ __________ _____ _______ ___ __________.
__________ ______ _________ ______ _________ ______.
Get Full Answer on WhatsApp