Which of the following equations can represent a triangle - Vidyadip

MCQ

Which of the following equations can represent a triangle

A
$|z - 1|\, = \,|z - 2|$
✓
$|z - 1| = |z - 2| = |z - i|$
C
$|z - 1| - |z - 2| = 2a$
D
$|z - 1{|^2} + |z - 2{|^2} = 4$

✓

Answer

Correct option: B.

$|z - 1| = |z - 2| = |z - i|$

b
(b)$|z - 1| = |z - 2| = |z - i|$
$(i)$ $|z - 1| = |z - i|$
represents a straight line through origin i.e., $y = x$
$(ii) $ $|z - 1| = |z - 2| \Rightarrow x = \frac{3}{2}$
which is a straight line
$(iii) $ $|z - 2| = |z - i| \Rightarrow 4x - 2y = 3$
which is a straight line
$|z - 1| = |z - 2| = |z - i|$ can represent a triangle.

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