If Aa-Bb- Cc- are vertices of - ABC of then coordinates of centroid are

The correct option is D g⃗=a⃗+b⃗+c⃗3 Given vertices a⃗,b⃗,c⃗ centroid(g) is the point from which the distance between centroid and vertices are equal ...

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Byju's Answer

Standard IX

Mathematics

The Mid-Point Theorem

If Aa⃗,Bb⃗,...

Question

If $A (\to a), B (\to b), C (\to c)$ are vertices of $Δ A B C$ of then coordinates of centroid are

\to g = \frac{\to a + \to b + \to c}{3}

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\to g = \to a + \to b + \to c

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\to g = \frac{\to a - \to b - \to c}{3}

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\to g = \to a - \to b + \to c

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Solution

The correct option is D $\to g = \frac{\to a + \to b + \to c}{3}$
Given vertices $\to a, \to b, \to c$
centroid(g) is the point from which the distance between centroid and vertices are equal
distance $A G$
$A G = \to g - \to a$ -------(1)
distance $B G$
$B G = \to g - \to B$ -------(2)
distance $C G$
$C G = \to g - \to c$ -------(3)
then
$A G + B G + C G$
$\to g - \to a + \to g - \to b + \to g - \to c = 0$
$3 \to g - (\to a + \to b + \to c) = 0$
$3 \to g = \to a + \to b + \to c$
$\to g = \frac{\to a + \to b + \to c}{3}$

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If A(→a),B(→b),C(→c) are vertices of ΔABC of then coordinates of centroid are

If $A (\to a), B (\to b), C (\to c)$ are vertices of $Δ A B C$ of then coordinates of centroid are