8. Is there a parallel translation in which the point M (3; - 5) goes to the point N (1; -4), and the point K (0; 0) - to the point L(-2; 1)?

Solution:
1. To find if a translation exists, the translation vector should be the same for both points.

2. Calculate the translation vector for points M to N:
- Translation vector: \vec{T_1} = (N_x - M_x, N_y - M_y) = (1 - 3, -4 + 5) = (-2, 1)

3. Calculate the translation vector for points K to L:
- Translation vector: \vec{T_2} = (L_x - K_x, L_y - K_y) = (-2 - 0, 1 - 0) = (-2, 1)

4. Compare the translation vectors:
- \vec{T_1} = (-2, 1)
- \vec{T_2} = (-2, 1)

5. Since \vec{T_1} = \vec{T_2}, the translation vector is the same for both sets of points.

6. Hence, the parallel translation exists and it is given by the vector (-2, 1).