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MHT CET202617 April 2026Morning ShiftMathematicsStraight LinesActual

If A(2, -3) and C(-6, 7) are opposite vertices of a rhombus ABCD, then the equation of diagonal BD is

Options

  1. A5x - 4y + 2 = 0
  2. B5x + 4y + 2 = 0
  3. C4x - 5y + 18 = 0
  4. D4x + 5y + 18 = 0

Correct answer

C. 4x - 5y + 18 = 0

Step-by-step solution

The diagonals of a rhombus bisect each other at right angles. Thus, diagonal BD is the perpendicular bisector of diagonal AC . The midpoint of diagonal AC is ( 2 - 6 2 , -3 + 7 2 ) = (-2, 2) . The slope of diagonal AC is m_ AC = 7 - (-3) -6 - 2 = 10 -8 = - 5 4 . Since BD AC , the slope of diagonal BD is m_ BD = - 1 m_ AC = 4 5 . The equation of diagonal BD , which passes through the midpoint (-2, 2) with slope 4 5 , is: y - 2 = 4 5 (x - (-2)) 5(y - 2) = 4(x + 2) 5y - 10 = 4x + 8 4x - 5y + 18 = 0

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