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Distances between Special Points in a Triangle

If z1= 3+2i...

Question

If $z_{1} = 3 + 2 i, z_{2} = 4 + 4 i, z_{3} = 5 + 6 i,$ then $z_{1}, z_{2}, z_{3}$ represents the vertices of a/an

A

right angle triangle

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B

equilateral triangle

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C

Isosceles triangle

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D

None of these

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Solution

The correct option is D None of these
Consider
$z_{1} + z_{3}$
$= 8 + 8 i$
$= 2 (4 + 4 i)$
$= 2 z_{2}$
Thus $z_{1}, z_{2}, z_{3}$ lie on a line.
Hence he answer is none of these.

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