p1
p2
p3
p4
p4 = p1 +
a(p2-p1) + b(p3-p1)
A(p4)+ t =
A(p1+a(p2-p1) + b(p3-p1)) + t
= A(p1)+t + a(A(p2)+t –
A(p1)-t) + b(A(p3)+t – A(p1)-t)
p4 is linear
combination of p1,p2,p3. Transformed
p4 is same linear combination of transformed
p1, p2, p3.
We call
(a,b) affine coordinates of p4.