The points $A,B,C$ represent the complex number $z_1,z_2$ and $(1-i)z_1+iz_2$ respectively on the complex plane. Then triangle $ABC$ is:
$(A)$ Isosceles but not right angled
$(B)$ Right angled but not isosceles
$(C)$ Isosceles and right angled
$(D)$ None of these
Could someone give slight hint as how to proceed in this question?