Q. 20 C5.0( 2 Votes )

# Verify the follow

Answer :

**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

BC = AD

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**

Rate this question :

Determine the poiRD Sharma - Mathematics

Let (3, 4, -1) anRD Sharma - Mathematics

The length of theRD Sharma - Mathematics

If P (0, 1, 2), QRD Sharma - Mathematics

Show that the triMathematics - Exemplar

Write the length RD Sharma - Mathematics

If the distance bRD Sharma - Mathematics

Find the point onRD Sharma - Mathematics

Find the point onRD Sharma - Mathematics

Write the coordinRD Sharma - Mathematics