Advertisement Remove all ads

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

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

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).

Advertisement Remove all ads

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
  Is there an error in this question or solution?

APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 14
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×