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Example1: Translate a square ABCD along with the coordinates as: A(0,0),B(5,0),C(5,5),D(0,5) via 2 units in x-direction and 3 units in y-direction.
Solution: We can show the square here, in matrix form, by using homogeneous coordinates of vertices as:
The translation factors are, tx=2, ty=3
The transformation matrix for translation:
Tv=
So new object point coordinates are:
[A'B'C'D'] = [ABCD].Tv
Hence, A'(x'1,y'1)=(2,3)
B'(x'2,y'2)=(7,3)
C'(x'3,y'3)=(7,8) and
D'(x'4,y'4)=(2,8)
determine the form of the transformation matrix for a reflection about an arbitrary line with equation y=mx+b.
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