ABC is an isosceles triangle. If the coordinates of the base are B(1,3) and  C(−2,7),the coordinates of vertex A can be

Let the vertex of triangle be A(x,y) ABC is an isosceles triangle. Therefore, (x−1)2+(y−3)2=(x+2)2+(y−7)2or 6x−8y+43=0Thus, any point lying on this line can be the vertex A except the midpoint (−12,5) of BC. Hence, vertex Ais (56,6).