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Please help me work out this C1 - Coordinate Geometry Question

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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Zacken
22
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 6−25−q\frac{6-2}{5-q}.

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

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

i.e: 6−25−q×2+1?−?=−1\frac{6-2}{5-q} \times \frac{2 + 1}{? - ?} = -1. Now solve for qq.
always try & do a sketch. with 2 dimensional coordinates it is straightforward.
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ghosteh
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Original post by Zacken

i.e: 6−25−q×2+1?−?=−1\frac{6-2}{5-q} \times \frac{2 + 1}{? - ?} = -1. Now solve for qq.


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.
Reply 4
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Zacken
22
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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ghosteh
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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
Reply 6
Avatar for Zacken
Zacken
22
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! :smile:
Reply 7
Avatar for ghosteh
ghosteh
OP
1
Original post by Zacken
So that's correct, then. Well done! :smile:


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 :smile:
Reply 8
Avatar for Zacken
Zacken
22
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 :smile:


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. :smile:

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