A Euclidean transformation $E$ sends the point $A = (0, 0)$ to the point $E(A) = (1, 1)$, the point $B = (1, 0)$ to the point $E(B) = (1, 2)$, and the point $C = (0, 1)$ to the point $E(C) = (2, 1)$.
Find equations of lines $l_1, l_2$ and $l_3$ such that the transformation $E$ can be represented by a reflection in the line $l_1$, followed by a reflection in the line $l_2$, followed by a reflection in the line $l_3$.
I'm told it is a glide reflection and the solution I've been provided is:
$l_1= y=-1$
$l_2=x=1$
$l_3=y=1$
But I have tried obtaining the image from these and it's not possible. I was wondering if there was a mistake in the solution or if I am not seeing something myself. I got
$l_1= y=x-1$
$l_2=y=-2$
$l_3=y=-1$
This seems to work but when reading it says a glide reflection is achieved by a reflection in a line followed by reflections in two lines, both of which are perpendicular to the original, but these are not so I am not sure if it's right?
The given solution is wrong. Let's look at point $A$. Reflection through $l_1$ yields $(0,-2)$. Then when reflected through $l_2$ you get $(2,-2)$. The last step $l_3$ yields $E(A)=(2,5)\ne(1,1)$