SOLUTION: The position of an ant and a spider in a room are A(2,3,5) and S(6,0,8) Determine the distance OS and OS if O is a point in a room represented by O(1,0,2)

Algebra ->  Length-and-distance -> SOLUTION: The position of an ant and a spider in a room are A(2,3,5) and S(6,0,8) Determine the distance OS and OS if O is a point in a room represented by O(1,0,2)      Log On


   

Question 1204339: The position of an ant and a spider in a room are A(2,3,5) and S(6,0,8) Determine the distance OS and OS if O is a point in a room represented by O(1,0,2)
Found 2 solutions by math_tutor2020, mananth:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer:
Exact distance = sqrt%2861%29
Approximate distance = 7.8102497

Explanation

The two points we focus on are
O = (x%5B1%5D, y%5B1%5D, z%5B1%5D) = (1,0,2) and S = (x%5B2%5D, y%5B2%5D, z%5B2%5D) = (6,0,8)

Let's plug those coordinates into the 3D version of the distance formula.


d+=+sqrt%28%281-6%29%5E2%2B%280-0%29%5E2%2B%282-8%29%5E2%29

d+=+sqrt%28%28-5%29%5E2%2B%280%29%5E2%2B%28-6%29%5E2%29

d+=+sqrt%2825%2B0%2B36%29

d+=+sqrt%2861%29

d+=+7.8102497 This value is approximate. Round this however needed.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The position of an ant and a spider in a room are A(2,3,5) and S(6,0,8) Determine the distance OS and OA if O is a point in a room represented by O(1,0,2)
To find the distance between A(x1,y1,z1)
and B(x2,y2,z2) , we use the formula:
AB=sqrt((x2−x1)^2+(y2−y1)^2+(z2−z1)^2)
For d(OS)
O(1,0,2), S(6,0,8)
OS=sqrt((6-1)^2+(0-0)^2+(8-2)^2)
= sqrt(5^2+6^2)
= sqrt(61) units
the distance between O and S (OS) is sqrt(61) units.

Similarly find OA