Find the centroid of the triangle ABC, if the mid-points of the sides BC,CA and AB are respectively (a,0,0),(0,b,0) and (00,c),`abc ne0`.

Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of the area of the triangle formed to the area of the given triangle

Find the coordinates of the centroid of a triangle the mid points of whose sides are (1,2,-3), (3,0,1) and (-1,1,-4)

The mid-points of the sides of a triangle are (1, 5, -1),(0,4,-2) and (2, 3, 4). Find its vertices.

The centroid of a triangle ABC is at the point (1,1,1). If the coordinates of A and B are (3,-5,7) and (-1,7,-6) respectively, find the coordinats of the point C.

The coordinates of the mid-points of the sides of DeltaPQR , are (3a,0,0), (0,3b,0) and (0,0,3c) respectively, then the area of DeltaPQR is

If D,E and F are the mid-points of the sides BC,CA and AB, respectively of a DeltaABC and O is any point, show that (i) AD+BE+CF=0

Let the area of a given triangle ABC be Delta . Points A_1, B_1, and C_1 , are the mid points of the sides BC,CA and AB respectively. Point A_2 is the mid point of CA_1 . Lines C_1A_1 and A A_2 meet the median BB_1 points E and D respectively. If Delta_1 be the area of the quadrilateral A_1A_2DE , using vectors or otherwise find the value of Delta_1/Delta

Find the incentre of the triangle with vertices A(1,sqrt3), B(0,0) and C(2,0) .

The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1), (1, 1) and (1, 0) is