Question

Points $A,B$ and with affixes $z_1,z_2$ and $(1-i)z_1+i{z}_2$ are the vertices of

• A. An isosceles traingle
• B. An equilateral triangle
• C. A right triangle
• D. An obtuse angled triangle

Answer 1

Answer: (A), (C)

The correct options are
A An isosceles traingle
C A right triangle

Let $A=i$ and $B=1$.
So, $C=(1-i)z_1+i{z}_2=(1-i)i+1=i+1+1=i+2$
So, $|AC|=2$, $|BC|=\sqrt{1^2+1^2}=\sqrt{2}$ and $|AB|=\sqrt{1^2+1^2}=\sqrt{2}$.
Thus, it is an isosceles right angles triangle since 2 sides are equal and it satisfies Pythagoras' theorem.
Hence, (a), (c) are correct.