Question

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

Answer 1

Answer:

(3 , 3 , 1)

Step-by-step explanation:

Given,

A = (2 , 4 , -1)

B = (3 , 6 , -1)

C = (4 , 5 , 1)

Let,

D = (x , y , z)

To Find :-

Co-ordinates of fourth vertex(D).

Solution :-

According to properties of Parallelogram Origin(O) is the mid-point of both AC and BD

Note :- Refer to the above picture.

Mid point Formula :-

M = $\sf\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2},\dfrac{z_1+z_2}{2}\bigg)$

O is mid - point of AC :-

O = $\sf\bigg(\dfrac{2+4}{2},\dfrac{4+5}{2},\dfrac{-1+1}{2}\bigg)$

O = $\sf\bigg(\dfrac{6}{2},\dfrac{9}{2},\dfrac{0}{2}\bigg)$

O = (3 , 9/2 , 0)

O is mid - point of BD also :-

(3 , 9/2 , 0) = $\sf\bigg(\dfrac{3+x}{2},\dfrac{6+y}{2},\dfrac{-1+z}{2}\bigg)$

3 = (3+x)/2 and 9/2 = (6+y)/2 and 0 = (-1+z)/2

6 = 3+x and 9 = 6+y and 0 = -1 + z

x = 3 and y = 3 and z = 1

D = (x , y , z) = (3 , 3 , 1)