# Math

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The points A(1, -2, 4), B(3, 5, 7), C(4, 6, 8) are three of four vertices of parallelogram ABCD. Determine the coordinates of vertex D

Could someone please tell me to go about solving this question. Thanks a lot.

• Math -

Calculate vector BA and add it to point C to get point D, similar to sliding the line BA until it fits on C.
Vector BA
= coordinates of A - coordinates of B.
=(1,-2,4) - (3,5,7)
=(-2,-7,-3)

You can take it from here.

Do check your calculations by comparing the mid-points of AC and BD. They should be identical since the diagonals of a parallelogram bisect each other.

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