ABC is an isosceles triangle. If the coordinates of the Base are B(1,3) and C(-2,7), then the coordinates of A will be

Question

Using the simple distance formula $$(x-1)^2+(y-3)^2=(x+2)^2+(y-7)^2$$ $$6x-8y+43=0$$ Obviously, the point will lie on this line. However, is it possible to find the exact the coordinates of A? Can this question be meaningfully solved?

Answer 1

Find the line that goes through points B and C and then find the line perpendicular to this line that passes through the mid-point of line BC. Then any point on this perpendicular line (A) will form and isosceles triangle with ABC (except when it's the mid-point of BC since it's obviously a line there).