Q. Let $\mathcal{z}_{1},\ \mathcal{z}_{2},\ \mathcal{z}_{3}$ be the affixes of the vertices of a triangle having the circumcentre at the origin. If $\mathcal{z}$ is the affix of it’s orthocentre, then $\mathcal{z}$ is equal to
A) $\frac{\mathcal{z}_{1} + \mathcal{z}_{2} + \mathcal{z}_{3}}{3}$
B) $\frac{\mathcal{z}_{1} + \mathcal{z}_{2} + \mathcal{z}_{3}}{2}$
C) $\mathcal{z}_{1} + \mathcal{z}_{2} + \mathcal{z}_{3}$
D) None of these
Explanation
(c)
Let $O$ is orthocenter, $G$ is centroid and $C$ is circumcentre, then
[image:5_image6.emf]
$\ \frac{\mathcal{z}_{1} + \mathcal{z}_{2} + \mathcal{z}_{3}}{3} = \frac{2 \times 0 + 1(\mathcal{z)}}{3}$
$\mathcal{\Rightarrow \ \ z =}\mathcal{z}_{1} + \mathcal{z}_{2} + \mathcal{z}_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.