In the projective space $P^3(\mathbb{K})$ with the frame $(S_0,S_1,S_2,S_3;E)$, consider a projective transformation as follows: $$\begin{cases} tx_0'=x_0\\ tx_1'=-x_1\\ tx_2'=-x_2\\ tx_3'=x_3.\end{cases}$$ Choose the plane at infinity $(S_1S_2S_3)$. What affine transformation does the above projective transformation correspond to?
Four affine transformations include reflection, glide reflection, rotation, and translation.
I have proved that the above projective transformation preserves the coordinate plane $(S_1S_2S_3)$. I don't know how to continue. Any help I would be very appreciated. Thanks in advance.
