# If the Centroid of δAbc Having Vertices a (A,B) , B (B,C) and C (C,A) is the Origin, Then Find the Value of (A+B+C). - Mathematics

If the centroid of ΔABC having vertices  A (a,b) , B (b,c) and C (c,a) is the origin, then find the value of (a+b+c).

#### Solution

The given points are A (a,b) , B (b,c) and C (c,a)

Here,

(x_1 = a , y_1=b),(x_2 = b, y_2 =c) and (x_3 = c, y_3= a)

Let the centroid be  (x , y) .

Then,

x= 1/3(x_1 +x_2 +x_3)

= 1/3 (a+b+c)

=(a+b+c)/3

y= 1/3 (y_1+y_2+y_3)

=1/3 (b+c+a)

=(a+b+c)/3

But it is given that the centroid of the triangle is the origin. Then, we have

=(a+b+c)/3 = 0

⇒ a+b+c =0

Concept: Area of a Triangle
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 14
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