Analytical Geometry

Jasonbot

macrumors 68020
Original poster
Aug 15, 2006
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The Rainbow Nation RSA
I'm writing a maths exam tomorrow and came across this problem I can't do...

P(-3;10) and Q(3;4) are vertices of triangle PQR. If the angle at Q= 90* determine the possible coordinates or R if QR= 4sqrt2 (sqrt32).

I've tried the distance formula for point on a cartesian plane but then I get an equation with x's and y's which I cant do. I understand that there must be two answers because the line could go up or down on the angle with the distance being equal.

The answer in the book is R1=(1;2) and R2=(5;7)

Oh and this will be my last exam for the mid year exam period :D
 

sammich

macrumors 601
Sep 26, 2006
4,283
212
Sarcasmville.
High school geometry...those were the days!

What you can simply do is find the equation for the line that is perpendicular to the line QP and passes through Q. It should be x + y = 1.

Then all you do with that is use the distance formula, use the relationship above to eliminate x or y, then solve!
 

Jasonbot

macrumors 68020
Original poster
Aug 15, 2006
2,467
0
The Rainbow Nation RSA
High school geometry...those were the days!

What you can simply do is find the equation for the line that is perpendicular to the line QP and passes through Q. It should be x + y = 1.

Then all you do with that is use the distance formula, use the relationship above to eliminate x or y, then solve!
wow! SO simple!

So...

[distance formula]=x+1. Should work. It seems logical!

EDIT: nope :(
heres what I did:

sqrt[(x-3)^2+(y-4)^2]=x+1
(x^2-6x+9)-(y^2-8y+16)=x^2+2x+1
-y^2+8y-8-6x=0

Its not working :(
 

siurpeeman

macrumors 603
Dec 2, 2006
6,311
18
the OC
*edit*
thought about it some more...

the slope of PQ = -1, which means that the slope of QR = +1. the line that contains both Q and R is y=x+1 (using +1 for slope going through (3,4)). so, R is to have coordinates (x, x+1), which you use distance formula with Q to equal root 32, or use distance formula with P to equal root 104. incidentally, my answers are:

R = (-1,0) and (7,8). i checked the first one. too lazy/tired to check the second.


*edit #2*
psh, no gratitude. :mad: :p
 

elfin buddy

macrumors 6502a
Sep 16, 2001
608
0
Tuttlingen, Germany
I'm writing a maths exam tomorrow and came across this problem I can't do...

P(-3;10) and Q(3;4) are vertices of triangle PQR. If the angle at Q= 90* determine the possible coordinates or R if QR= 4sqrt2 (sqrt32).

I've tried the distance formula for point on a cartesian plane but then I get an equation with x's and y's which I cant do. I understand that there must be two answers because the line could go up or down on the angle with the distance being equal.

The answer in the book is R1=(1;2) and R2=(5;7)

Oh and this will be my last exam for the mid year exam period :D
Just from checking the answers your book gives, I guarantee your book is wrong. The lengths of the QR sides are off by a factor of 2 from the problem requirements.

My calculations indicate that siurpeeman's answer is correct. I solved the problem from scratch and got the same answers as him.
 

ErikCLDR

macrumors 68000
Jan 14, 2007
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I used to know how to do this last year or the year before. But its summer, so all gained knowledge has gone into deep storage.
 

Mac One

macrumors member
Jul 18, 2007
71
0
NZ
Well I got the same answer as you guys... not that it's of any use now.

Good luck for your exam Jasonbot, hope it goes OK
What year are you in? I did that sort of stuff last year. (I'm in my final year now.)

Enjoy not having any more exams!
 

Jasonbot

macrumors 68020
Original poster
Aug 15, 2006
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The Rainbow Nation RSA
Mac One said:
Well I got the same answer as you guys... not that it's of any use now.

Good luck for your exam Jasonbot, hope it goes OK
What year are you in? I did that sort of stuff last year. (I'm in my final year now.)

Enjoy not having any more exams!
Yeh, I'm in form 4 now. We have a total of five forms and the school year is from january to december.

Well I'm on holiday now but I get my exam results next wednesday *holds breath*