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