Opposite Side Equation of Rhombus

CAT 2000 Slot 1 · QA · Medium · Coordinate Geometry

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ABCDABCD is a rhombus with the diagonals ACAC and BDBD intersecting at the origin on the x-y plane. The equation of the straight line ADAD is x+y=1x + y = 1. What is the equation of BCBC?

  1. A.

    x+y=−1x + y = -1

  2. B.

    x−y=−1x - y = -1

  3. C.

    x+y=1x + y = 1

  4. D.

    None of these

Answer

A

Explanation

In a rhombus whose diagonals intersect at the origin, opposite sides ADAD and BCBC are parallel and symmetric about the origin. Since ADAD has equation x+y=1x + y = 1, the opposite side BCBC is parallel to ADAD and at an equal distance on the opposite side of the origin, so its equation is x+y=−1x + y = -1.

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