Q. 20 C5.0( 2 Votes )

# Verify the follow

Given: Points are A(-1, 2, 1), B(1,-2, 5), C(4, -7, 8) and D(2, -3, 4)

To prove: the quadrilateral formed by these 4 points is a parallelogram

Opposite sides of a parallelogram are equal, but diagonals are not equal

Formula used:

The distance between any two points (a, b, c) and (m, n, o) is given by, Therefore,

Distance between A(-1, 2, 1) and B(1,-2, 5) is AB,    = 6

Distance between B(1,-2, 5) and C(4, -7, 8) is BC,    Distance between C(4, -7, 8) and D(2, -3, 4) is CD,    = 6

Distance between A(-1, 2, 1) and D(2, -3, 4) is AD,    Clearly,

AB = CD

Opposite sides are equal

Now, we will find the length of diagonals

Distance between A(-1, 2, 1) and C(4, -7, 8) is AC,    Distance between B(1, -2, 5) and D(2, -3, 4) is BD,    Clearly,

AC BD

The diagonals are not equal, but opposite sides are equal

Thus, Quadrilateral formed by ABCD is a parallelogram

Hence Proved

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