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Three vertices of a parallelogram are (0, 0), (3, 5) and (6, 2). The fourth vertex equals:
A(6, 5)
B(9, 7)
C(3, 2)
D(7, 9)
Answer & Solution
Correct answer: B. (9, 7)
1. If the parallelogram is ABCD with A = (0,0), B = (3,5), D = (6,2), the fourth vertex C lies opposite A.
2. By the textbook rule, in a parallelogram OBCD with O at origin, C = B + D = (3+6, 5+2) = (9, 7).
3. The diagonals of a parallelogram bisect each other, and this rule encodes that condition.
4. So C = (9, 7).
5. None of the other choices satisfy the diagonal-bisection property.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._
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