What is the isometric reflection of $M∩A_t$ across $P_t$ in the poincaré model?

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Could anyone help me to understand what is $(M ∩ A_t)'$, ie, the isometric reflection of $M∩A_t$ across $P_t$? Here's the article I'm reading below:enter image description here

Article pdf: https://arxiv.org/pdf/0804.4211.pdf