Finding the transformation matrix for a specific transformation of a line(computer graphics), how does this work?

[shivajikobardan]

Line A(0,0) and B(1,1). After transformation A'(0,-1) and B'(-1,0).
Now I need to find the transformation matrix.
Imagine the 2d transformation matrix is 2x2
[a b]
[c d]
Then,
we get for A->A'
a.0+b.0=0
c.0+d.0=-1

This equation can never be solved as 0 can never be equals to -1....
Let us do for the other point B.
We get
a+b=-1
c+d=0

So a and b can be anything for example a=-1 and b=0. But what about c and d? How to solve for them?

 

[Dr.Peterson]

Line A(0,0) and B(1,1). After transformation A'(0,-1) and B'(-1,0).
Now I need to find the transformation matrix.

Please state the problem exactly as given. Clearly it can't be asking for a transformation represented by multiplication by a matrix; you've shown that's impossible. What sort of transformation is specified?

 

[shivajikobardan]

I already got it. The question is as clear as it can get. Affine transformation is the keyword.

 

[Dr.Peterson]

I already got it. The question is as clear as it can get. Affine transformation is the keyword.

That's what I expected. So you don't need any more help? Good.