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1998

JEE Main 1998 Mathematics question on Straight Lines and Pair of Lines

If P(1,2)P(1,2), Q(4,6)Q(4,6), R(5,7)R(5,7) and S(a,b)S(a,b) are the vertices of a parallelogram PQRSPQRS, then
  1. A.
    a=2,b=4a = 2, b = 4
  2. B.
    a=3,b=4a = 3, b = 4
  3. C.
    a=2,b=3a = 2, b = 3
  4. D.
    a=3,b=5a = 3, b = 5
Show answer and solution

Correct option: C

Solution

In a parallelogram, diagonals bisect each other, so the midpoint of PR equals the midpoint of QS.

Midpoint of PR = ((1+5)/2, (2+7)/2) = (3, 9/2)
Midpoint of QS = ((4+a)/2, (6+b)/2)

Setting equal: (4+a)/2 = 3 → a = 2, and (6+b)/2 = 9/2 → b = 3.

[1998]

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