How to show that f is a glide reflection?

Question

Suppose that A=(0,1) B=(0,0) C=(1,0).

f(A) = (1.8,1.6), f(B) = (1,1), and f(C) = (0.4,1.8).

How do I know that this is a glide reflection?

I can tell that f is not a translation, because the two lines Af(A) and Bf(B) are not parallel. If I can also show that f is not a rotation, then f should be a glide reflection, but I don't know how.

Anyone one can help? thx.

Answer 1

In a (glide) reflection, the midpoint between $P$ and $f(P)$ lies on the line which defines the transformation. So you just need to check that the three midpoints of $Af(A)$, $Bf(B)$, $Cf(C)$ are aligned.

Answer 2

I found the solution here: http://mduchin.math.tufts.edu/UCD/141/sols.pdf, in problem 3.7.4

It says, Check if it has the same orientation as the original triangle with vertices A,B,C by checking if going from A to B to C is clockwise or counterclockwise in the first triangle, and checking similarly for the image triangle. If the orientations are different, it must be a glide reflection.