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Question: The three angular points of a triangle are given by Z = a, Z = b, Z = g, where a, b, g are complex n...

The three angular points of a triangle are given by Z = a, Z = b, Z = g, where a, b, g are complex numbers, then the perpendicular from the angular point Z = a to opposite side is given by the equation :

A

Re(Z−αβ−γ)\left( \frac{Z - \alpha}{\beta - \gamma} \right) = 1

B

Re(Z−αβ−γ)\left( \frac{Z - \alpha}{\beta - \gamma} \right) = 0

C

Re(Z−αβ−γ)\left( \frac{Z - \alpha}{\beta - \gamma} \right) = – 1

D

Re(Z−αβ−γ)\left( \frac{Z - \alpha}{\beta - \gamma} \right) = 2

Answer

Re(Z−αβ−γ)\left( \frac{Z - \alpha}{\beta - \gamma} \right) = 0

Explanation

Solution

Sol. Since AD ⊥\bot BC

Žarg (α–Zγ–β)\left( \frac{\alpha –Z}{\gamma –\beta} \right) = π2\frac{\pi}{2}

Žarg(Z−αβ−γ)\left( \frac{Z - \alpha}{\beta - \gamma} \right) = π2\frac{\pi}{2}

ŽZ−αβ−γ\frac{Z - \alpha}{\beta - \gamma}is purely imaginary

or Re(Z−αβ−γ)\left( \frac{Z - \alpha}{\beta - \gamma} \right) = 0