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# Coordinate Geometry

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1. Here is question which I'm stuck on:

A triangle has vertices P(-2,2), Q(q,0) and R(5,3).
The side PQ is twice as long as side QR.
Find the possible values of q.

How do I answer this question??
2. (Original post by krisshP)
Here is question which I'm stuck on:

A triangle has vertices P(-2,2), Q(q,0) and R(5,3).
The side PQ is twice as long as side QR.
Find the possible values of q.

How do I answer this question??
Try it in terms of vectors. I can post a start if you want it.
3. PQ=2QR

What is the length of the line PQ? What is the length of the line QR?

Post some working.
4. (Original post by notnek)
PQ=2QR

What is the length of the line PQ? What is the length of the line QR?

Post some working.

Am I heading the right way?? Shall I continue from here?
5. (Original post by krisshP)

Am I heading the right way?? Shall I continue from here?
That's correct so far. Now write down the length of PQ in terms of q.

6. Now what???
7. (Original post by krisshP)

Now what???
What is PQ? Use the same method as you used to find QR.
8. ok notnek I will.

Now what do I do??
9. (Original post by krisshP)
ok notnek I will.

Now what do I do??
Now square both sides so you get:

Can you simplify and solve this?
10. (Original post by notnek)
Now square both sides so you get:

Can you simplify and solve this?
I'll try to do the rest.

Thanks a lot for your help
11. (Original post by notnek)
Now square both sides so you get:

Can you simplify and solve this?
I end up with the following:

Is this right?? Can I still solve it??
12. (Original post by krisshP)
I end up with the following:

Is this right?? Can I still solve it??
That's correct. You can tidy the equation up and make it easier to solve by multiplying it by -4.
13. (Original post by notnek)
That's correct. You can tidy the equation up and make it easier to solve by multiplying it by -4.
I get the following:

Is it ok for me to divide both sides by 3 and use the completing the square method?

q=4 and q=32/3

Thanks a lot Notnek for your help
15. (Original post by krisshP)
I get the following:

Is it ok for me to divide both sides by 3 and use the completing the square method?
You can use that method here but I've always been more of a fan of factorising:

If you really aren't able to factorise then completing the square is OK to use.
16. (Original post by krisshP)
I get the following:

Is it ok for me to divide both sides by 3 and use the completing the square method?
That, or using the quadratic formula. (or factorising, of course, hadn't checked it to see if it did)

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