Question

vertex.
Find the fourth vertex of the parallelogram whose consecutive vertices are
(2, 4, -1), (3, 6, -1), (4,5,1)
​

Answer 1

Answer:

here is your answer

hope this will help for you

Answer 2

Given:

Vertices of a parallelogram:

(2, 4, -1), (3, 6, -1), (4, 5, 1)

To find:

Fourth vertex of the parallelogram

Solution:

Let the vertices of the parallelogram in order be A(2, 4, 1), B(3, 6, -1), C(4, 5, 1), and D(x, y, z).

Then we have two diagonals BD and AC.

The mid-point of BD can be written as follows,

$(\frac{3+x}{2}, \frac{6+y}{2} , \frac{-1+z}{2} )$

and mid-point of AC is as follows,

$(\frac{2+4}{2} ,\frac{4+5}{2}, \frac{-1+1}{2})=(3, \frac{9}{2}, 0)$

In a parallelogram, the two diagonals bisect each other. So, we can write,

$\frac{3+x}{2}=3$, $\frac{6+y}{2}=\frac{9}{2}$, $\frac{-1+z}{2}=0$

⇒$x=3, y=3, z=1$

So, the fourth vertex of the parallelogram is $(3, 3, 1)$.