Question

Show that the points (5,-1,1),(7,-4,7),(1,-6,10),(-1,-3,4)
are the vertices of rhombus.​

Answer 1

Answer:

Solution

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

Therefore,

Distance between A(5, -1, 1) and B(7, -4, 7) is AB,

= 7

Distance between B(7, -4, 7) and C(1, -6, 10) is BC,

= 7

Distance between C(1, -6, 10) and D(-1, -3, 4) is CD,

= 7

Distance between A(5, -1, 1) and D(-1, -3, 4) is AD,

= 7

Clearly,

AB=BC=CD=AD

All sides are equal

Now, we will find length of diagonals

Distance between A(5, -1, 1) and C(1, -6, 10) is AC,

Distance between B(7, -4, 7) and D(-1, -3, 4) is BD,

Clearly, AC



=BD

The diagonals are not equal, but all sides are equal

Thus, Quadrilateral formed by ABCD is a rhombus

Hence Proved