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JEE Main 2016

JEE Main 2016 Mathematics question on Straight Lines and Pair of Lines

Two sides of a rhombus are along the lines, x−y+1=0x - y + 1 = 0 and 7x−y−5=07x - y - 5 = 0. If its diagonals intersect at (−1,−2)(-1, -2), then which one of the following is a vertex of this rhombus?
  1. A.
    (−3,−9)(-3, -9)
  2. B.
    (−3,−8)(-3, -8)
  3. C.
    (13,−83)\left(\frac{1}{3}, -\frac{8}{3}\right)
  4. D.
    (−103,−73)\left(-\frac{10}{3}, -\frac{7}{3}\right)
Show answer

Correct option: C

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