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The fourth vertex of a parallelogram with three given vertices (1, 3), (5, 4), (2, 5) is (taking the missing vertex opposite (1, 3)):
Answer & Solution
Correct answer: C.
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.)._
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