Discussion Forum

A parallelogram has vertices A(4,4,-1), B(5,6,-1),C(6,5,1) and D(x,y,z) . Then the vertex D is 

Answer:

Explanation:

Given , ABCD is a parallelogram with vertices  A(4,4,-1), B(5,6,-1), C(6,5,1) and D(x,y,z)

 We know that digonals  of parallelogram ABCD bisects each other. 

  $\therefore$  Mid poinr of Ac= Mid point of BD

 $\Rightarrow$          $\left(\frac{4+6}{2},\frac{4+5}{2},\frac{-1+1}{2}\right)=\left(\frac{x+5}{2},\frac{y+6}{2},\frac{z-1}{2}\right)$

$\Rightarrow$         $\left(\frac{10}{2},\frac{9}{2},0\right)=\left(\frac{x+5}{2},\frac{y+6}{2},\frac{z-1}{2}\right)$

On comparing both sides, we get

      $\frac{x+5}{2}=\frac{10}{2},\frac{y+6}{2}=\frac{9}{2}$ and $\frac{z-1}{2}=0$

$\Rightarrow$   $x+5=10,y+6=9$ and $z-1=0$

$\Rightarrow$   $x=10-5,y=9-6$ and z=1

$\Rightarrow$   x=5 ,y=3 and z=1

Thus ,        D(x,y,z)=D(5,3,1)