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Math Help - Finding the distance between points

  1. #1
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    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.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Finding the distance between points

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

    So in this case the disctance is given by:
    d=\sqrt{[a-(a+h)]^2+[\sqrt{a}-\sqrt{a+h}]^2}
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  3. #3
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    Re: Finding the distance between points

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

    So in this case the disctance is given by:
    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?
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  4. #4
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    Re: Finding the distance between points

    Quote Originally Posted by riderk View Post
    ok... my text book and this website says sqrt((x2-x1)^2 + (y2-y1)^2) am I missing something or is this a typo?
    Quote Originally Posted by riderk View Post
    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: x_1=a,~x_2=a+h thus x_2-x_1=h

    y_1=\sqrt{a},~y_2=\sqrt{a+h} thus y_2-y_1=\sqrt{a+h}-\sqrt{a}
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  5. #5
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    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 (\sqrt{a}- \sqrt{a+h})^2 and Siron has (\sqrt{a+h}- \sqrt{a})^2 but they are the same: (a- b)^2= (-(b-a))^2= (b- a)^2.
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  6. #6
    MHF Contributor Siron's Avatar
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    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 .
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