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Thread: Vector of P magnitude: O(0,0), A(-1,3), B(-5,4), C(7,P)

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    Vector of P magnitude: O(0,0), A(-1,3), B(-5,4), C(7,P)

    Hello, I have four points O (0,0) A(-1,3) B(-5,4) and C(7,P)

    I have found vector AC to be (8, (p-3))

    Now the question is stating what are the values of P for which '' l Vector AC l '' (those two vertical lines are included)=10

    Im guessing this is th magnitude so I sub it into the formula which would be (sqrt) (82+(p-3)2)= 10

    But from here I keep failing and I am not sure what to do, because I keep ending up with (sqrt) (64 + (p-3)2) =10
    And if I try to solve (p-3)2 = 0 to get values for P I would end up with P=3 and then my answer for the equation would just not give me the correct answer.

    How do i solve this?
    Last edited by richiesmasher; 02-28-2018 at 03:03 PM.

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    Quote Originally Posted by richiesmasher View Post
    And if I try to solve (p-3)2 = 0
    Could you clarify where this came from?

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    Quote Originally Posted by lev888 View Post
    Could you clarify where this came from?
    It didnt come from anywhere, I just figured to solve the overall equation I could solve that equation separately first.

    SO I know (p-3)2 is a perfect square

    So: (p-3) (p-3) =0

    Each value of p would be then 3

    So I used that in the equation i guess?

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    Quote Originally Posted by richiesmasher View Post

    SO I know (p-3)2 is a perfect square

    So: (p-3) (p-3) =0
    Yes, I was asking how you figured out that the next step would be that equation. I don't quite understand the reasoning. First, I don't see any requirements that (p-3)2 should be a perfect square. And even if it is, why 0?

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    Quote Originally Posted by lev888 View Post
    Yes, I was asking how you figured out that the next step would be that equation. I don't quite understand the reasoning. First, I don't see any requirements that (p-3)2 should be a perfect square. And even if it is, why 0?
    Idk because it's a quadratic?

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    Quote Originally Posted by richiesmasher View Post
    Idk because it's a quadratic?
    Just try to solve sqrt(82+(p-3)2) = 10 without any assumptions. Hint: sqrt(x) = 10. What is x?

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    Quote Originally Posted by lev888 View Post
    Just try to solve sqrt(82+(p-3)2) = 10 without any assumptions. Hint: sqrt(x) = 10. What is x?
    x = (82+(p-3)2)

    So therefore this

    (82+(p-3)2)= 100

    Am I on to something?
    Last edited by richiesmasher; 02-28-2018 at 05:30 PM.

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    Quote Originally Posted by richiesmasher View Post


    Am I on to something?

    Looks good, keep going.

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    Quote Originally Posted by lev888 View Post
    Looks good, keep going.
    (82+(p-3)2)=100
    64+p2-6p+9=100

    p2-6p-27=0

    p2+3p-9p-27=0

    p(p+3)-9(p+3)

    Therefore :

    (p+3) (p-9)=0

    p = 9 and p=-3


    Last edited by richiesmasher; 02-28-2018 at 06:22 PM.

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    Check the last step.

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