Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x - y + z = 5 .Statement-2: The plane x - y + z = 5 bisects - Mathematics MCQ AIEEE 2026 | ExamTest.live

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Statement-1: The point A (3, 1, 6) is the mirror image of the point B (1, 3, 4) in the plane x - y + z = 5 .Statement-2: The plane x - y + z = 5 bisects the line segment joining A (3, 1, 6) and B (1, 3, 4) .

A $Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1.$
B $Statement-1 is true, Statement-2 is false.$
C $Statement-1 is false, Statement-2 is true.$
D $Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1.$

Solution & Step-by-step Explanation

For A to be the mirror image of B :The midpoint of A B must lie on the plane.Midpoint = (\frac{3 + 1}{2}, \frac{1 + 3}{2}, \frac{6 + 4}{2}) = (2, 2, 5) .Plane: 2 - 2 + 5 = 5 . (Satisfied).The vector A B must be parallel to the normal of the plane. A B = (3 - 1) \hat{i} + (1 - 3) \hat{j} + (6 - 4) \hat{k} = 2 \hat{i} - 2 \hat{j} + 2 \hat{k} .Normal to plane n = \hat{i} - \hat{j} + \hat{k} .Since A B = 2 n, it is parallel.Statement-1 is True. Statement-2 is also True (the midpoint lying on the plane means the plane bisects the segment), and it is a necessary part of the explanation.

Try it yourself before checking the explanation above.

Statement-1: The point A (3, 1, 6) is the mirror image of the point B (1, 3, 4) in the plane x - y + z = 5 .Statement-2: The plane x - y + z = 5 bisects the line segment joining A (3, 1, 6) and B (1, 3, 4) .

Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1.

Statement-1 is true, Statement-2 is false.

Statement-1 is false, Statement-2 is true.

Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1.

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