Question

Show that the points (5.-1,1),(7,-4,7),(1,-6,10) and (-1,-3,4)are the vertices of a rhombus

Answer 1

Step-by-step explanation:

Given Show that the points (5.-1,1),(7,-4,7),(1,-6,10) and (-1,-3,4)are the vertices of a rhombus

• We have a rhombus ABCD and AB = BC = CD = DA
• But AC^2  is not equal to AB^2 + BC^2
• So angle B will not be equal to 90 degree
• So the points are A = (5,-1,1), B = (7,-4,7), C = (1,-6, 10) and D = (1,-3,4)
• So AB = √2^2 + 3^2 + 6^2
•            = √49
•           = 7 units
• BC = √6^2 + 2^2 + 3^2
•       = √49
•       = 7 units
• CD = √2^2 + 3^2 + 6^2
•       = √49
•       = 7 units
• DA = √6^2 + 2^2 + 3^2
•       = √49
•       = 7 units.
• So we have AB = BC = CD = DA
• Now by checking we get
• AC = √4^2 + 5^2 + 9^2
•        = √122
• AB^2 + BC^2 = 7^2 + 7^2
•                           = 49 + 49
•                           = 98  
• This is not equal to AC^2
• Therefore angle ABC is not equal to 90 degree.
• Hence this is a rhombus.

Reference link will be

https://brainly.in/question/13032838