SOLUTION: A point ({{{ 3sqrt(5)}}}, d+3 ) is 3d units away from the origin. What is the smallest possible value of d?

Algebra ->  Coordinate-system -> SOLUTION: A point ({{{ 3sqrt(5)}}}, d+3 ) is 3d units away from the origin. What is the smallest possible value of d?      Log On


   

Question 1068660: A point (+3sqrt%285%29, d+3 ) is 3d units away from the origin. What is the smallest possible value of d?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the distance formula to find the distance from the origin,
D%5E2=%283sqrt%285%29-0%29%5E2%2B%28%28d%2B3%29-0%29%5E2
D%5E2=45%2B%28d%2B3%29%5E2
But you know that D=3d
9d%5E2=45%2Bd%5E2%2B6d%2B9
8d%5E2-6d-54=0
4d%5E2-3d-27=0
%284d%2B9%29%28d-3%29=0
Only a positive d makes sense in this problem,
d-3=0
d=3