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This is a very simple calculation. For a start, you can assume that $B=(0,0)$, $C=(1,0)$ and $A=(p,q)$. $A‘$ is thus $(p,tq)$. The computations are then very easy, or, if this is too difficult, one can reduce to the case $p=1$, i.e., that of a right triangle. I doubt if you will find a reference for anything this trivial—-you certainly don‘t require the monographs mentioned above.