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Three vertices of a parallelogram ABCD are A(4, 0, 3), B (3, 4, – 2) and C (– 2, 0, 1). find the coordinate of fourth vetex.

Three vertices of a parallelogram ABCD are A(4, 0, 3), B (3, 4, – 2) and C (– 2, 0, 1). find the coordinate of fourth vetex.

Grade:Upto college level

1 Answers

Latika Leekha
askIITians Faculty 165 Points
6 years ago
The vertices of the paralleologram ABCD are A(4, 0, 3), B (3, 4, – 2) and C (– 2, 0, 1).
Since in a parallelogram, the opposite sides are equal as well as parallel, so we must have AB = DC.
Now, coordinates of A and B are A(4, 0, 3), B (3, 4, – 2).
Hence, AB = (-1, 4, -5).
CD = - AB = (1, -4, 5).
Hence, the coordinates of D are (1, -4, 5) + (-2, 0, 1)
= (-1, 4, 6)
Thanks & Regards
Latika Leekha
askIITians Faculty

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