Three vertices of a parallelogram ABCD are A(1, 2, 3) , B(-1, -2, -1) and C(2, 3, 2) . The coordinates of the fourth vertex D are: - Mathematics MCQ Mathematics Mock Test - 11 2026 | ExamTest.live

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Three vertices of a parallelogram A BC D are A (1, 2, 3), B (- 1, - 2, - 1) and C (2, 3, 2) . The coordinates of the fourth vertex D are:

Solution & Step-by-step Explanation

In a parallelogram A BC D, the diagonals A C and B D bisect each other at the same midpoint.Midpoint of A C : M = (\frac{1 + 2}{2}, \frac{2 + 3}{2}, \frac{3 + 2}{2}) = (1.5, 2.5, 2.5) Let D be (x, y, z) . Midpoint of B D must be M : \frac{x + ( - 1 )}{2} = 1.5 ⟹ x - 1 = 3 ⟹ x = 4 \frac{y + ( - 2 )}{2} = 2.5 ⟹ y - 2 = 5 ⟹ y = 7 \frac{z + ( - 1 )}{2} = 2.5 ⟹ z - 1 = 5 ⟹ z = 6 The coordinates of D are (4, 7, 6) .

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Three vertices of a parallelogram A BC D are A (1, 2, 3), B (- 1, - 2, - 1) and C (2, 3, 2) . The coordinates of the fourth vertex D are:

(- 2, - 3, 0)

(4, 7, 6)

(2, 3, 4)

(- 2, - 3, 4)

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