Question

the vertices of parallelogram abcd are A(4,0,3), B(3,4,-2),C(-2,0,1). find the coodrdinates of fourth vertices

Answer 1

Given :

The vertices of parallelogram ABCD are A(4,0,3), B(3,4,-2),C(-2,0,1).

To Find :

The coordinates of fourth vertices.

Solution :

We know, the vertices are ABCD .

Let, point D is (x,y,z) .

Also, diagonals of a parallelogram bisect each other.

Let, point of intersection of daigonal is O.

Coordinates of O are :

$O_x = \dfrac{4+(-2)}{2}= 1\\\\O_y = \dfrac{0+0}{2 } = 0 \\\\O_z = \dfrac{3+1}{2}= 2$

O(1,0,2)

Value of point O through BD.

$O_x = \dfrac{3+x}{2}\\\\x=-1\\\\O_y = \dfrac{4+y}{2}\\\\y = -4\\\\O_z= \dfrac{-2+z}{2}\\\\z = 6$

Therefore, the fourth vertices is D( -1,-4,6 ).