# The isomerty f maps points, determine f.

The isometry f maps points (0,0), (1,0) and (0,1) into (3,3), (3,4) and (4,3).

1. Determine f in the form f = Ax+b

2. Are there any fixed points of f, and hence determine whether f is a translation, rotation, reflection or glide-reflection.

Attempt: I equated the transformed coordinates x' with transformation Ax+b to get $$A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$$ and $$b = [3,3]^{T}$$ Is this correct?

Also I couldn't understand part 2, can you please explain it? Thank You.

Edit: For the second part, I deduced the transformation was glide- reflection. The transformation f first translates along line $$y=x$$ by 3 units and then reflects along the same line, hence it appears to be a glide - reflection. As for the fixed points of f, what does in this context? Are the common points among original and transformed coordinates called fixed points or is there any other criteria.

• I think there is a mistake. It looks like the points are mapped in the wrong order. – Kavi Rama Murthy Jul 3 at 9:34
• @KaviRamaMurthy you are right, thank you. I edited now. – DubsVeer23 Jul 3 at 9:36

Your matrix $$A$$ is not correct. Correct is
$$A = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}.$$
Hence $$f(x)=x+(3,3)^T.$$ This shows that $$f$$ has no fixed points.