Question

Show that the four points A (5,-1,1), B (7,-4,7), C (1, -6, 10) and D (-1, -3, 4) are the vertices of a parallelogram.

Answer 1

use the distance formula for the given vertices

Answer 2

Answer:

AB ║ CD & AB = CD  & BC ║ DA & BC = DA

=> ABCD is an parallelogram

Step-by-step explanation:

Show that the four points A (5,-1,1), B (7,-4,7), C (1, -6, 10) and D (-1, -3, 4) are the vertices of a parallelogram.

Correction -6.10 is actually -7

AB = √(7-5)² + (-4.7 -(-1.1))² = √ 4 + 12.96 = √16.96

m = (-4.7 - (-1.1)/(7-5) = -3.6/2 = -1.8

CD = √2² + 3.6² = √16.96

m = (-3.4 - (-7) )/(-1 -1) = 3.6/-2 = -1.8

Hence AB ║ CD & AB = CD

BC = √6² + 2.3² = √41.29

m = (-7 - (-4.7) )/(1 - 7) = -2.3 /-6 = 2.3/6

DA = √6² + 2.3² = √41.29

m = (-3.4 -(-1.1))/(-1 - 5) = -2.3/-6 = 2.3/6

Hence BC ║ DA & BC = DA

AB ║ CD & AB = CD  & BC ║ DA & BC = DA

=> ABCD is an parallelogram

so ABCD are vertices of an parallelogram