The vertices of a triangle are A (9,2), B(1,10) and C(-7,-6)
Here, x1 = 9, x2 = 1, x3 = -7
and y1 = 2, y2 = 10, y3 = -6
Let the coordinates of the centroid be(x,y)
So,
= (1,2)
Hence, the centroid of a triangle is (1, 2)
Now,
Let D, E and F are the midpoints of the sides BC, CA and AB respectively.
The coordinates of D are:
F = (5, 6)
Now, we find the centroid of a triangle formed by joining these middle points D, E, and F as shown in figure
Let P be the trisection point of the median AD which is nearer to the opposite side BC
∴ P divides DA in the ratio 1:2 internally
= (1, 2)
Let Q be the trisection point of the median BE which is nearer to the opposite side CA
∴ Q divides EB in the ratio 1:2 internally
= (1, 2)
Let R be the trisection point of the median CF which is nearer to the opposite side AB
∴ R divides FC in the ratio 1:2 internally
= (1, 2)
Yes, the triangle has the same centroid, i.e. (1,2)