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Math Help - Distance Expression

  1. #1
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    Distance Expression

    Hey guys, I'm just needing a little help. Winter break definitely rusted up my brain.
    What expression represents the distance from Point A (2,4) to Point C (10,d)?

    I'm also needing help with this...

    For what value of a is the line x + ay=26 parallel to the line 2x-4y=13?
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  2. #2
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    d(P,Q) = \sqrt {\left( {x_P  - x_Q } \right)^2  + \left( {y_P  - y_Q } \right)^2 } .

    If we have a line Ax + By + C = 0 it has slope \frac{{ - A}}{B}.
    Two parallel lines have the same slope.
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  3. #3
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    Quote Originally Posted by Plato View Post
    d(P,Q) = \sqrt {\left( {x_P  - x_Q } \right)^2  + \left( {y_P  - y_Q } \right)^2 } .

    I'm sorry, I must just be really slow at this. How can I tell which is P and which is Q?
    Would is be (2-4)^2 and (10-d)^2? Like 64 + 10d?
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  4. #4
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    Quote Originally Posted by lemon301 View Post
    I'm sorry, I must just be really slow at this. How can I tell which is P and which is Q?
    Would is be (2-4)^2 and (10-d)^2? Like 64 + 10d?
    Ok now swap P and Q, then substitute in the formula and simplify...
    The question is, does it matter which is which?
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  5. #5
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    Quote Originally Posted by lemon301 View Post
    I'm sorry, I must just be really slow at this. How can I tell which is P and which is Q?
    Would is be (2-4)^2 and (10-d)^2? Like 64 + 10d?
    Hi,

    that doesn't matter because for instance

    (4-2)^2 = (2-4)^2
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  6. #6
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    I'm trying to plug it in the formula you gave and so far I have (square root) 64 + d but should it be (square root) 64 + (d-4)^2?
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  7. #7
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    Quote Originally Posted by lemon301 View Post
    I'm trying to plug it in the formula you gave and so far I have (square root) 64 + d but should it be (square root) 64 + (d-4)^2?
    Yes,

    \sqrt{(d-4)^{2}+64}
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