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  • Three vertices of a parallelogram ABCD are A(3, – 1, 2), B (1, 2, – 4) and C (– 1, 1, 2). Find the coordinates of the fourth vertex.

1. Three vertices of a parallelogram ABCD are A(3, – 1, 2), B (1, 2, – 4) and C (– 1, 1, 2). Find the coordinates of the fourth vertex.

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Given three vertices of the parallelogram ABCD, they are:

A (3,  -1, 2), B (1, 2, -4), and C (-1, 1, 2).

Let the fourth vertice be (a, b, c ) 

Now, as we know the concept that the diagonals of the parallelogram bisect each other,

Hence, in parallelogram ABCD, the midpoint of the line segment AC will be equal to the midpoint of the line segment BD.

So,

\left ( \frac{3-1}{2},\frac{-1+1}{2},\frac{2+2}{2} \right )=\left ( \frac{1+a}{2},\frac{2+b}{2},\frac{-4+c}{2} \right )

On comparing both points, we get

a=1,b=-2\:and\:c=8

Hence, the fourth vertice of the is (1,-2,8)

Posted by

Pankaj Sanodiya

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