Question

If the centroid of the triangle formed with (a, b), (b, c) and (c, a) is O(0,0), then find the value of a + b + c​

Answer 1

Answer:

a + b + c = 0

Step-by-step explanation:

Centroid of triangle Formula:

• G ( x,y ) = ( [ x₁ + x₂ + x₃ ] / 3 , [ y₁ + y₂ + y₃ ] / 3 )

According to the question:

• x₁ = a
• x₂ = b
• x₃ = c

Also it is given that x coordinate of Centroid is 0.

⇒ ( a + b + c ) / 3 = 0

⇒ a + b + c = 0 × 3

⇒ a + b + c = 0

Therefore the value of a + b + c is 0.

Hope it helped !!

Answer 2

$\huge\sf{Answer:-}$

To solve this question easily let us use the centroid triangle formula.

Formula:-

• $\sf G = (x\: or\: y)$
• $\sf G = x1,x2,x3/3$
• $\sf G = y1,y2,y3/3$

Given question ,

Let

• $\sf y1 = a ,$
• $\sf y2 = b \:and$
• $\sf y3 = c$

Hence,

Using formula we get,

$\sf (a+b+c / 3 = 0)$

$\sf (a+b+c = 0 × 3) = (a+b+c=0)$

$\bf Hence,value\: of\: (a+b+c\: is \:equal \:to\: 0)$

Formula used to answer this question

$\sf [Centroid \:of\: triangle\: formula.]$