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If {z}_{1},{z}_{2},{z}_{3} are affixes of the vertices A,B and

Question

If $z_{1}, z_{2}, z_{3}$ are affixes of the vertices $A, B$ and $C$ respectively of a triangle $A BC$ having centroid at $G$ such that $z = 0$ is the midpoint of $A G$ , then

z_{1} + z_{2} + z_{3} = 0

z_{1} + 4 z_{2} + z_{3} = 0

z_{1} + z_{2} + 4 z_{3} = 0

4 z_{1} + z_{2} + z_{3} = 0

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Owen Discussed

z_{1}, z_{2}, z_{3}

are affixes of the vertices

A, B

and

C

respectively of a triangle

A BC

having centroid at

G

such that

z = 0

is the midpoint of

A G

, then

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Text solutionVerified

Let the co-ordinates of

A, B

and

C

(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})

Centroid of

△ A BC = \frac{z _{1} + z _{2} + z _{3}}{3}

Since, it is given

z = 0

is the mid-point of

A G

\Rightarrow

⎝ ⎛ \frac{z _{1} + \frac{z _{1} + z _{2} + z _{3}}{3}}{2} ⎠ ⎞ = 0

\Rightarrow

\frac{3 z _{1} + z _{1} + z _{2} + z _{3}}{6} = 0

∴

4 z_{1} + z_{2} + z_{3} = 0

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Question Text	If $z_{1}, z_{2}, z_{3}$ are affixes of the vertices $A, B$ and $C$ respectively of a triangle $A BC$ having centroid at $G$ such that $z = 0$ is the midpoint of $A G$ , then
Answer Type	Text solution:1
Upvotes	150