For f(t)= (t/sqrt(t+1),t^2-t) what is the distance between f(0) and f(2)?

1 Answer
Nov 29, 2017

(4sqrt(3))/3

Explanation:

f(0) = (0/(sqrt(0+1)), 0^2-0)
= (0, 0)
f(2) = (2/(sqrt(2+1)), 2^2-2)
= (2/sqrt(3), 2)
Let's use the distance formula. In case you don't know what it is, here it is:
The distance d between (a, b) and (c, d) is:
d = sqrt((d-b)^2 + (c-a)^2).
We can apply this to our problem. Using the distance formula,
d = sqrt((2-0)^2 + (2/sqrt(3)-0)^2)
= sqrt((2^2) + (2/sqrt(3))^2)
=sqrt(4 + 4/3)
=sqrt(12/3 + 4/3)
=sqrt(16/3)
=4/sqrt(3)
=(4sqrt(3))/3 (if you want to rationalize the denominator)