The fourth vertex of a parallelogram with three given vertices (1, 3), (5, 4), (2, 5) is (taking the missing vertex opposite (1, 3)):

1. In any parallelogram, the diagonals bisect each other. 2. So midpoint of diagonal joining (1, 3) and (x, y) = midpoint of diagonal joining (5, 4) and (2, 5). 3. Midpoint of the second diagonal = ((5+2)/2, (4+5)/2) = (3.5, 4.5). 4. So (1 + x)/2 = 3.5 → x = 6; and (3 + y)/2 = 4.5 → y = 6. 5. The fourth vertex is therefore (6, 6). _Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._