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JEE Main202623 January 2026Evening ShiftMathematicsStraight LinesActual

Let A (1,2) and C (-3,-6) be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line 7 x-y=14 . If B ( , ) and D ( , ) are the other two vertices, then | + + + | is equal to

Options

  1. A6
  2. B9
  3. C3
  4. D1

Correct answer

A. 6

Step-by-step solution

Midpoint of diagonal AC is M = (-1,-2) . Slope of AC = -6-2 -3-1 = 2 . In a rhombus, diagonals are perpendicular bisectors. So BD has slope - 1 2 and passes through M : y + 2 = - 1 2 (x+1) . AD has slope 7: - 2 - 1 = 7 = 7 - 5 . D lies on BD : = - 2 - 5 2 . Solving: 7 - 5 = - 2 - 5 2 = 1 3 , = - 8 3 . B = (2(-1)- 1 3 , , 2(-2)+ 8 3 ) = (- 7 3 , - 4 3 ) . | + + + | = |- 7 3 - 4 3 + 1 3 - 8 3 | = |-6| = 6 .

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