I was working through a few locus questions and I can't seem to find how finding the d(distance formula for perp lines- ie abs(ax+bx+c)/sqrta^2+b^2) of two points can give an equation of a locus, why is that? I'll provide a example.
This is not relevant:
"(distance formula for perp lines- ie abs(ax+bx+c)/sqrta^2+b^2) "
The formula you seem to be referring to is finding the smallest distance of a point from a line.
What is being used here is Pythagoras theorem.
To answer your question in the image. We need to equate the two distances because this is part of the constraint imposed for the locus. Then just as it magically turns out we get a line after simplification.
Another potential solution is just find the perpendicular bisector of AB. This works because of Pythagoras theorem. Try visualizing it on the coordinate plane
