Points M (-2; -1), N (-3; 1), K (0; 1) are given. Find the coordinates of point P knowing that MNKP is a parallelogram.

The coordinates of the point P are equal to the coordinates of the point M in the sum with the coordinates of the vector MP. By condition, MNPK is a parallelogram, which means that the sum of the vectors MN and MK is equal to the vector МР. And therefore, the sums of the coordinates of the vectors MN and MK are equal to the coordinates of the vector МР.

Using the coordinates of the points M, N and K, we find the coordinates of the vectors MN, MK, MP and the required coordinates of the point P:

MN: (-3 – (-2); 1 – (- 1)) = (-1; 2),

MK: (0 – (-2); 1 – (- 1)) = (2; 2),

MR: (-1 + 2; 2 +2) = (1; 4),

P (-2 + 1; -1 + 4) = P (-1; 5).

Answer: P (-1; 5).