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  • Three consecutive vertices of a parallelogram ABCD are A (6, – 2, 4), B (2, 4, – 8), C (–2, 2, 4). Find the coordinates of the fourth vertex

Three consecutive vertices of a parallelogram ABCD are A (6, – 2, 4), B (2, 4, – 8), C (–2, 2, 4). Find the coordinates of the fourth vertex

Answers (1)

Let us assume that the coordinates of the fourth vertex D is (x,y,z).

Now, mid-point of diagonal AC = P(6-2/2, -2+2/2,4+4/2)

                                               = P(2,0,4)

Since it is a parallelogram, the mid-point of BD will also be P,

                                               = P(x+2/2,y+4/2,z-8/2)

                                               = P(2,0,4)

Now, let us equate the coordinates of P,

X+2/2 = 2, i.e., x = 2;

Y+4/2 = 0, i.e., y = -4;

Z-8/2 = 4, i.e., z = 16

Therefore, the coordinates of D will be (2,-4,16).

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