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MHT CET202526 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

The mirror image of the point P (-1,2,-4) in the plane x- y -2 z +1=0 is

Options

  1. A(3,-4,1)
  2. B(-3,4,0)
  3. C(4,1,0)
  4. D(2,-3,0)

Correct answer

B. (-3,4,0)

Step-by-step solution

Mirror image of a point in a plane Given point P(-1, 2, -4) and plane x - y - 2z + 1 = 0 , the mirror image Q(x', y', z') is found using the foot of the perpendicular M from P to the plane as the midpoint of PQ . The coordinates of M follow from the formula x_M + 1 1 = y_M - 2 -1 = z_M + 4 -2 = - (1)(-1) + (-1)(2) + (-2)(-4) + 1 1^2 + (-1)^2 + (-2)^2 . Simplifying the denominator gives 1 + 1 + 4 = 6 , and the numerator evaluates to -1 - 2 + 8 + 1 = 6 , so the ratio is -1 . Solving for M : x_M + 1 = -1 x_M = -2 , y_

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