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1. 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.
2. (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 .

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

i.e: . Now solve for .
3. always try & do a sketch. with 2 dimensional coordinates it is straightforward.
4. (Original post by Zacken)
i.e: . Now solve for .
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.
5. (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.
6. (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
7. (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!
8. (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
9. (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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