Question

If (-1, 2), (2, -1) and (3, 1) are three vertices of a parallelogram, then the coordinate of fourth vertice is

Answer 1

Let the coordinates of vertices of paralellogram be A(−1,2),B(3,1),C(2,−1) and D(a,b)
The points A and B can be either vertices of one side or opposite corners of one diagonal.
We know diagonals of a parallelogram bisect each other.

1st case: A and B are vertices of a side.

2nd case: A and B are opposite corners of a diagonal.

3rd case: C and B are opposite corners of a diagonal.