Question

the centroid of the triangle formed by (a,b) (2a,2b) (3a,3b) is

Answer 1

Given:

Triangle formed by (a,b) (2a,2b) (3a,3b)

To find:

The centroid of the given triangle.

Solution:

1) The Centroid of a triangle is an intersection point of the three medians of the triangle.

2) The centroid of the triangle having coordinates (x1,y1), (x2,y2) and (x3,y3) is given by:

• Centroid(X,Y) = $(\frac{x1+x2+x3}{3}),(\frac{y1+y2+y3}{3})$

• (X,Y) = a+2a+3a/3, b+2b+3b/3

• (X,Y) = 6a/3, 6b/3

• (X,Y) = (2a,2b)

The centroid of the given triangle is (2a,2b).

Answer 2

Given : triangle formed by (a,b) (2a,2b) (3a,3b)

To find   :   centroid of the triangle

Solution:

centroid of the triangle formed by intersection of Median

Hence centroid always lies with in the triangle

Centroid  = (x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3

for three vertices ( x₁, y₁) , (x₂ , y₂)  & (x₃ , y₃)

Here Vertices are

(a,b) (2a,2b) (3a,3b)  

Centroid  = (a + 2a + 3a)/3 , ( b + 2b + 3b)/3

= 2a , 2b

(2a , 2b) is the vertex of triangle  and  not lying inside

Hence this should not be Centroid of Triangle

It Means there is some mistake in Given Data :

Lets Check Triangle data

(a,b) (2a,2b) (3a,3b)  

Length of Side of Triangle  =   √a² + b²  ,  √a² + b²   , 2√a² + b²

Sum of two Sides = Third Side

Hence points are Colinear  

( or we can check slope between any pair of point is Same =  b/a   , hence points are colinear )

And No Triangle will be formed by these points

Hence no Centroid of Triangle

We can Say Data is wrong here as Triangle is not possible

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