Given,
The vertices of ΔABC = A, B and C
Coordinates of A, B and C;
A(x1, y1)
B(x2, y2)
C(x3, y3)
(i) As per given information D is the mid - point of BC and it bisect the line into two equal parts.
Coordinates of the mid - point of BC;
Given,
The point P(x, y), divide the line joining A(x1, y1) and D in the ratio 2:1
Then,
(iii) ∴ Let the coordinates of a point Q be (p, q)
Given,
The point Q (p, q),
Divide the line joining B(x2, y2) and E in the ratio 2:1,
Then,
Since, BE is the median of side CA, So BE divides AC in to two equal parts.
∴ mid - point of AC = Coordinate of E;
Now,
Let the coordinates of a point E be (⍺, β)
Given,
Point R (⍺, β) divide the line joining C(x3, y3) and F in the ratio 2:1,
Then the coordinates of R;
(iv) Coordinate of the centroid of the ΔABC;