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Thread: Locus Question

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    Cadet Heresy's Avatar
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    Locus Question

    The question is as follows:
    "The gradient of the line between a moving point P(x,y) and the point A(5,3) is equal to the gradient of the line PB where B has coordinates (2,-1). Find the equation of the locus of P."

    Since I haven't done the Locus topic yet I'm really lost...
    This is from linear functions...

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    Member jathu123's Avatar
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    Re: Locus Question

    If the gradient of PA is equal to the gradient of PB, then P must lie on the line through A AND B. Otherwise the gradients of PA and PB will be different (you can draw up a diagram to visualise this). So in essense, the locus of P is equation of the line through A and B (as P can lie anywhere on this line such that m(PA) = m(PB))

    So find the gradient of AB and use the point gradient-formula to find the eqn of the line

    m = (-1-3)/(2-5) = 4/3

    therefore, y +1 = 4/3(x-2) [rearrange this and you're done]
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    Re: Locus Question

    Quote Originally Posted by jathu123 View Post
    If the gradient of PA is equal to the gradient of PB, then P must lie on the line through A AND B. Otherwise the gradients of PA and PB will be different (you can draw up a diagram to visualise this). So in essense, the locus of P is equation of the line through A and B (as P can lie anywhere on this line such that m(PA) = m(PB))

    So find the gradient of AB and use the point gradient-formula to find the eqn of the line

    m = (-1-3)/(2-5) = 4/3

    therefore, y +1 = 4/3(x-2) [rearrange this and you're done]
    Thank you so much mate!

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