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Math Help - Linear Algebra

  1. #1
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    Linear Algebra

    The point (h, k) lies on the line y = x + 1 and is 5 units from the point (0, 2). Write down two equations connecting h and k and hence find the possible values of h and k.

    I know that once I have two equations for h and k I need to solve them simultaneously to find the values, but the "5 units from the point (0, 2)" part of the question is confusing me. If you could point me off in the right direction I should be able to take it from there.

    Thanks in advance.
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  2. #2
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    Re: Linear Algebra

    Hi,
    First equation:

    k=h+1

    Second equation:

    \sqrt{h^2+(k-2)^2}=5 or h^2+(k-2)^2=25
    Thanks from Fratricide
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  3. #3
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    Re: Linear Algebra

    Hey Fratricide.

    Hint: In two dimensions, you can use the fact that m1*m2 = -1 for gradients m1 and m2 that are perpendicular to each other. The equation of a line in two dimensional space is y = mx + b or y - y0 = m(x - x0) for a known point (x0,y0) on the line. Basically using this you have two sets of equations that are independent which means you can solve for the intersected point.
    Thanks from Fratricide
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  4. #4
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    Re: Linear Algebra

    Quote Originally Posted by chiro View Post
    Hey Fratricide.

    Hint: In two dimensions, you can use the fact that m1*m2 = -1 for gradients m1 and m2 that are perpendicular to each other. The equation of a line in two dimensional space is y = mx + b or y - y0 = m(x - x0) for a known point (x0,y0) on the line. Basically using this you have two sets of equations that are independent which means you can solve for the intersected point.
    Reading John's post has left me indubitably confused.

    I know the equation of a line in two-dimensional space, as well how m1*m2 = -1, but I still can't figure out what to do.

    Thank you for your patience.
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  5. #5
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    Re: Linear Algebra

    Basically you have two equations:

    y = m1*x + b1
    y = m2*x + b2.

    You then solve for x and y and you have your point (h,k)

    Do you know how to get your m's and your b's?
    Thanks from Fratricide
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  6. #6
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    Re: Linear Algebra

    Fratricide ( you said : Reading John's post has left me indubitably confused.

    I know the equation of a line in two-dimensional space, as well how m1*m2 = -1, but I still can't figure out what to do.

    Thank you for your patience. )

    there is nothing wrong with john's post .contrary it is self explanatory...the coordinates h,k satisfy the equation y =x+1 . the second equation is the distance between the two points....solve the system of the symultaneous equations as supplied by John and you will find (h,k)=(-3,-2) or (4,5).
    Thanks from Fratricide
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  7. #7
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    Re: Linear Algebra

    Oh God, sorry about that. I was having a blond moment. Hahah. Woke up this morning and everything makes perfect sense.

    One last question: Chiro, are you hinting towards John's equations, or is there a different method that can be used that involves the equations you mentioned?

    Thanks everybody for your help.
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