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Question: z<sub>1</sub>, z<sub>2</sub>, z<sub>3</sub> are the affixes of the vertices of a triangle having its...

z1, z2, z3 are the affixes of the vertices of a triangle having its circumcentre at the origin. If z is the affix of its orthocenter, then -

A

z1 + z2 + z3 – z = 0

B

z1 + z2 – z3 + z = 0

C

z1 – z2 + z3 + z = 0

D

– z1 + z2 + z3 + z = 0

Answer

z1 + z2 + z3 – z = 0

Explanation

Solution

Sol. We know from Co-ordinate Geometry that the

Points O, G, H are collinear and that G divides OH in the ratio 1 : 2.

Hence by ratio formula

13\frac{1}{3} S z1 = 1.z+2.01+2\frac{1.z + 2.0}{1 + 2} = z3\frac{z}{3}

\ z1 + z2 + z3 – z = 0 Ž (1).