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 = (4+(-2))/(2)= 1\\\\O_y = (0+0)/(2 ) = 0 \\\\O_z = (3+1)/(2)= 2`

O(1,0,2)

Value of point O through BD.

`O_x = (3+x)/(2)\\\\x=-1\\\\O_y = (4+y)/(2)\\\\y = -4\\\\O_z= (-2+z)/(2)\\\\z = 6`

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