You have an isosceles triangle with points labelled ABC
"standing" vertically, so B is the apex at the top. The picture in only for communicating the point labelling, the triangle can be presented in any rotation, (if thought of as an arrow, it could be pointing at any angle) but an original orientation is not known. You know the coordinate pairs of A,B,C and which one of those pairs is B, but you don't know yet which pairs are A and which are C.
Figure out which of the two remaining coordinates is A and C, purely in terms of coordinates with only the points presented in trig level math, if possible.
Compute $$ \Delta=(x_C-x_A)(y_B-y_A)-(y_C-y_A)(x_B-x_A). $$ If $\Delta>0$ then $A$ and $C$ labels are in the right place, otherwise they must be exchanged.