Are my results correct?

Task:

Determine the coordinates of a point D such that the points A, B, C and D are the vertices of a parallelogram.

a). A(3|-2|4); B(7|2|1); C(4|6|6)

My solution: D(0|2|9)

b). A(8|4|9); B(4|-1|3); C(5|2|8)

My solution: D(9|7|14)

c). A(3|4|-2); B(-3|-4|2); C(0|0|0)

My solution: D(3|4|-2)

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Rammstein53
1 year ago

Deduction of point D:

Center of diagonal AC: M = (A+C)/2

The point D lies on the straight line B+2*(M-B)

D=B+2*(M-B)=2*M-B=A+C-B

The first two solutions are correct.

The last task is that A+B=C.

A,B,C lie on a straight line.

No parallelogram can be formed here

The theoretical solution would be D=6.8,-4)=2*A, also on the straight line. Your solution could have noticed that A=D