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If the centroid of ABC having vertices A(a, b), B(b, c) and C

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If the centroid of $Δ A BC$ having vertices $A (a, b), B (b, c)$ and $C (c, a)$ is the origin, then find the values of $(a + b + c)$ .

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If the centroid of

Δ A BC

having vertices

A (a, b), B (b, c)

and

C (c, a)

is the origin, then find the values of

(a + b + c)

9 mins ago

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Text solutionVerified

Centroid of

Δ A BC

having vertices

A (a, b) \equiv (x_{1}, y_{1}), B (b, c) \equiv (x_{2}, y_{2})

and

C (c, a) \equiv (x_{3}, y_{3})

is the origin.
Let

O (0, 0) \equiv (x, y)

is the centroid of

Δ A BC

.
And
Centroid

(x, y)

= \frac{x _{1} + x _{2} + x _{3}}{3}, \frac{y _{1} + y _{2} + y _{3}}{3}

0 = \frac{a + b + c}{3}

∴ a + b + c = 0

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Question Text	If the centroid of $Δ A BC$ having vertices $A (a, b), B (b, c)$ and $C (c, a)$ is the origin, then find the values of $(a + b + c)$ .
Answer Type	Text solution:1
Upvotes	150