Question

Find the locus of centeroid of triangle ABC if B(1,1), C(4,2) and A lies on the line Y = X + 3 ?

Answer 1

The locus of centroid of triangle will be: $y= x+\frac{1}{3}$

Explanation

The co ordinate of the vertices of triangle ABC are given as:  B(1, 1) and C(4, 2)

The vertex A lies on the line $y= x+3$

Suppose, there co ordinate of vertex A is (x, y) and the co ordinate of centroid is (h, k)

According to the formula of centroid.......

$(h,k)= (\frac{x+1+4}{3},\frac{y+1+2}{3}) \\ \\ (h,k)=(\frac{x+5}{3},\frac{y+3}{3})$

Now after comparing, we will get.......

$\frac{x+5}{3}=h\\ x+5=3h\\ x=3h-5\\ \\ and\\ \\ \frac{y+3}{3}=k\\ y+3=3k\\ y=3k-3$

So, the co ordinate of vertex A is : $(3h-5 , 3k-3)$

As this vertex is lying on line $y=x+3$, so the point will satisfy the equation. Thus.....

$3k-3=3h-5+3\\ \\ 3k-3=3h-2\\ \\ 3k=3h-2+3\\ \\ 3k=3h+1 \\ \\ k=h+\frac{1}{3}$

So, the locus of centroid of triangle will be: $y= x+\frac{1}{3}$

Answer 2

Answer:

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