If the midpoints of sides of the triangle PQR are (1,2) (0,1) (1,0), then find the cordinates of thevertices of the triangle.

Let be the vertices of the triangle ABC and be the mid points of sides AB, BC and CA respectively.

Since P is the mid point of side AB. Therefore,

Similarly, Q and R is the mid point of side BC and CA respectively. So,

And,

Adding equation (1), (3), (5) and (2), (4), (6), we get,

And,

Subtracting equation (1), (3) and (5) from equation (7) respectively, we get,

Subtracting equation (2), (4) and (6) from equation (8) respectively, we get,

Hence, the vertices of triangle ABC are A(2,1) , B(0,3) and C(0,-1).

**
**