Rectangle Diagonal Equation Parameter c

CAT 2017 Slot 2 · QA · Medium · Co-ordinate Geometry

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The points (2,5)(2, 5) and (6,3)(6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y=3x+cy = 3x + c, then cc is

  1. A.

    –5

  2. B.

    –6

  3. C.

    –7

  4. D.

    –8

Answer

D

Explanation

The diagonals of a rectangle bisect each other.

Midpoint of the given diagonal = (2+62,5+32)=(4,4)\left(\frac{2 + 6}{2}, \frac{5 + 3}{2}\right) = (4, 4).

The other diagonal must also pass through this midpoint (4,4)(4, 4).

Substitute (4,4)(4, 4) into y=3x+cy = 3x + c: 4=3(4)+c  ⟹  4=12+c  ⟹  c=−84 = 3(4) + c \implies 4 = 12 + c \implies c = -8.

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