# Thread: Finding the distance between points

1. ## Finding the distance between points

The question states find the distance between the following points (a,sqrt(a)) (a+h,sqrt(a+h))

To begin with i know i should plug it into the distance formula so..
sqrt((a+h-a)^2 + (sqrt(a+h)-sqrt(a))^2)

from here I subtract a from a+h leaving sqrt((h)^2 + (sqrt(a+h)-sqrt(a))^2)

I'm unsure of how to proceed from here. If I remeber correctly (sqrt(a+h)-sqrt(a) is already simplified so i would assume I multiply (sqrt(a+h)-sqrt(a) (sqrt(a+h)-sqrt(a) use foil and then add the (h)^2 to the product but that answer doesn't check.

I then tried to rationalize the numerator but that seems like i'm over complicating it. i've been trying to solve this off and on for a week now with no luck its just an optional homework assignment that isn't graded, but I would really like to know how to figure this out. Any help would greatly be appreciated.

2. ## Re: Finding the distance between points

The distance $\displaystyle d$ between two points $\displaystyle p_1(x_1,y_1)$ and $\displaystyle p_2(x_2,y_2)$ is given by the formula:
$\displaystyle d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

So in this case the disctance is given by:
$\displaystyle d=\sqrt{[a-(a+h)]^2+[\sqrt{a}-\sqrt{a+h}]^2}$

3. ## Re: Finding the distance between points

Originally Posted by Siron
The distance $\displaystyle d$ between two points $\displaystyle p_1(x_1,y_1)$ and $\displaystyle p_2(x_2,y_2)$ is given by the formula:
$\displaystyle d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

So in this case the disctance is given by:
$\displaystyle d=\sqrt{[a-(a+h)]^2+[\sqrt{a}-\sqrt{a+h}]^2}$
ok... my text book and this website says sqrt((x2-x1)^2 + (y2-y1)^2) am I missing something or is this a typo?

4. ## Re: Finding the distance between points

Originally Posted by riderk
ok... my text book and this website says sqrt((x2-x1)^2 + (y2-y1)^2) am I missing something or is this a typo?
Originally Posted by riderk
The question states find the distance between the following points (a,sqrt(a)) (a+h,sqrt(a+h))
Those two are exactly the same. There is no typo.
In this problem: $\displaystyle x_1=a,~x_2=a+h$ thus $\displaystyle x_2-x_1=h$

$\displaystyle y_1=\sqrt{a},~y_2=\sqrt{a+h}$ thus $\displaystyle y_2-y_1=\sqrt{a+h}-\sqrt{a}$

5. ## Re: Finding the distance between points

No, there is no typo. I don't see any difference between what you give and what Siron says. It is true that you have $\displaystyle (\sqrt{a}- \sqrt{a+h})^2$ and Siron has $\displaystyle (\sqrt{a+h}- \sqrt{a})^2$ but they are the same: $\displaystyle (a- b)^2= (-(b-a))^2= (b- a)^2$.

6. ## Re: Finding the distance between points

@ riderk:
My apologies in case of confusing you, but I couldn't read your answer well, but now I see you're right .