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Please help me work out this C1 - Coordinate Geometry Question Watch

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    Question: The straight line joining the point P(5, 6) to the point Q(q, 2) is perpendicular to the straight line joining the point Q to the point R(9, -1).
    Calculate the possible values for q

    Watched a few videos and read the examples from the book the question comes in but I can't figure out the right steps to go through for this question.

    Any help much appreciated.
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    (Original post by ghosteh)
    Question: The straight line joining the point P(5, 6) to the point Q(q, 2) is perpendicular to the straight line joining the point Q to the point R(9, -1).
    Calculate the possible values for q

    Watched a few videos and read the examples from the book the question comes in but I can't figure out the right steps to go through for this question.

    Any help much appreciated.
    What's the gradient of the line PQ in terms of q? It's \frac{6-2}{5-q}.

    What about the gradient of QR? It's \frac{2 -- 1}{? - ?}.

    Now you know that if they are perpendicular then the product of these two gradients is -1.

    i.e: \frac{6-2}{5-q} \times \frac{2 + 1}{? - ?} = -1. Now solve for q.
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    always try & do a sketch. with 2 dimensional coordinates it is straightforward.
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    (Original post by Zacken)
    i.e: \frac{6-2}{5-q} \times \frac{2 + 1}{? - ?} = -1. Now solve for q.
    Thanks for the reply, I have got that far on my own and this is where I am stuck. I can't seem to rearrange or multiply this out to make sense of it.

    Could you do the steps for me so I can see it. There is another question in the book which is very similar, so I can work through that one afterwards to see if I've understood.
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    (Original post by ghosteh)
    Thanks for the reply, I have got that far on my own and this is where I am stuck. I can't seem to rearrange or multiply this out to make sense of it.

    Could you do the steps for me so I can see it. There is another question in the book which is very similar, so I can work through that one afterwards to see if I've understood.
    Do you know how to multiply fractions? This should form a quadratic.
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    (Original post by Zacken)
    Do you know how to multiply fractions? This should form a quadratic.

    12 divided by -q^2 + 14q - 45 = - 1

    rearrange gets 12 = q^2 -14q + 45

    q^2 - 14q + 33 = 0

    (q - 11) (q - 3)

    q = 11 or 3

    -----------

    going back and substituting in those values I will find the products of the gradients = -1
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    (Original post by ghosteh)
    12 divided by -q^2 + 14q - 45 = - 1

    rearrange gets 12 = q^2 -14q + 45

    q^2 - 14q + 33 = 0

    (q - 11) (q - 3)

    q = 11 or 3

    -----------

    going back and substituting in those values I will find the products of the gradients = -1
    So that's correct, then. Well done!
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    (Original post by Zacken)
    So that's correct, then. Well done!
    Looking at it, I have no idea why I didn't just go through that straight away. Brain block.

    I suppose I should say thank you for not answering my question
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    (Original post by ghosteh)
    Looking at it, I have no idea why I didn't just go through that straight away. Brain block.

    I suppose I should say thank you for not answering my question
    That's what TSR is here for, to nudge and guide. Had I given you the full solution, you'd have been spoilt of the chance to get at it yourself.
 
 
 
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