It is not true that the best way to do geometry is by converting everything into algebra. Proving simple geometric stuff like, the three altitudes of a triangle

It is not true that the best way to do geometry is by converting everything into algebra. Proving simple geometric stuff like, the three altitudes of a triangle all intersect at a single point, is a pain using coordinates. Just because it's possible to convert problems in domain X into problems in domain Y doesn't mean that domain X is pointless.