Check whether (5,−2), (6,4) and (7,−2) are the vertices of an isosceles triangles.
Let ABC be the triangle A(5,−2),B(6,4),C(7,−2)
By distance formula
AB=√(5−6)2+(−2−4)2=√(−1)2+(−6)2√37
BC=√(6−7)2+(4−(−2)2=√(−1)2+(6)2=√37
CA=√(7−5)2+(−2−(−2))2=√(2)2+0=2
Since AB=BC=√37
Hence (5,−2),(6,4) & (7,−2) are vertices of isosceles triangle.