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Let PQR be a right angled isosceles triangle in a cartesian plane, right angled at P(2,1). If the equation of the line QR is 2x+y = 3, then the equation representing the pair PQ and PR is..

Mathematics
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Draw a picture first. it always helps visualize
Well there wasn't one but neway heres what I can do..
When it says right angled at (2,1) I think at that point it is 90 deg

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Other answers:

|dw:1347994216890:dw|
yes dats pretty obvious isn't it??
Right angle isoceles means that the sides to each side of the right angle are equal. Ya I'd say so after the picture.
yup, both the angles will be 45 degrees, i.e, 45+45+90
well ChmE??
well @ChmE
Can't anybody solve this??
Ok let me try.
I want to say PQ is just x=2 and PR is just y=1, but what if the triangle is at an angle..
just find points Q and R, given that we know P
then use point slope and all that business
Its an isosceles right angled triangle that means 2 of its angle are 45 degrees and one is at 90 degrees..
@TuringTest the question is HOW???
let's draw a bigger pic
|dw:1347994331965:dw|
btw the answers ae PQ = x+3y -5 and PR = 3x-y-5
lol does that help?
@bahrom7893 No dude!!! Its already in the question... :P
|dw:1347994441088:dw|
Yeah now what??
I got it so far!!! next step will be what??
at x=2 what is y ?
calm down dude I am explaining...
:P Sorry its just that its getting in my head bad!!
well all that is given in the ques, no additionally details are provided..
though I must admit I;m not sure exactly what they are asking the equation for the pair? what do they mean?
hahhahahahah.. Exactly what Ive stumbled upon..
by pair of lines they mean PQ and PR
but infinitely I assume, not a finite line segment....
nope its finite alright!!!
then the answer must give bounds to x and y
Look will it help if I write the solution down, The thing is Ive got the solution but I don't really understand it very well...
|dw:1347994766490:dw|
yeah that may help me understand what they are asking
The equations of PQ and Pr are... y-2 = [-2 -/+ tan 45/1+/- (-2)tan 45] * (x-2) <=> HOW??? Solving this they Got PQ ad PR...
PR*
oh I misinterpreted the problem I see
|dw:1347994998473:dw|so my assumption that the legs of the triangle followed the grid was wrong
@TuringTest Still don't get...
well now the problem is harder than I thought, so let me think on it I was eating lunch as I was doing this because I thought it would be easy lol
:P well it isn't @hartnn DUDE!!! You were saying u got it ryt?? Will you do the honor of telling me how??
even i thought that lines are vertical and horizontal.....but they r not.....even i m stuck...
that seems the formula for tan(A+B) ....in the solution u mentioned....do u have some standard formulas in this topic ?
I know!!! just one , but I don't understand hw to implement it in this one..
Two lines will be perpendicular to each other if...coeff of x^2 + coeff of y^2 = 0
but this is a first degreeequation so can't really put that in...
yes, that won't help..
Think people THINK!!!! The person who can solve this will be titled a born genius.. :P
|dw:1347995522447:dw|
I dunno I'll have to drop this for now...
NOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!! :'(
|dw:1347995617810:dw| i don't know what i m doing......
6 equations 8 unknowns.
:P
mM=-1--->7th equation.
1 more equation and we are done.
you mean one more equation if was provided??
1 more equation WE need to find.
Take all the time you need, Ill be here for a while....
lol, very big equation it is!! PQ=PR and distance formula :P
:P
we getting 8 equations and 8 unknowns but its almost impossible to solve them simultaneously.....there must be another way...
I typed in the equation and the solution that was given in the text.. The only questions bugging my mind is Y and HOW??
and even how y-2 and x-2 ?? y-2 and x-1 maybe.....
we can use help of @ganeshie8 here....
Is he any good??
you will see.
do u have formulas like this somewhere ? \(\huge y-y_1=\frac{m_1\pm m_2}{1\mp m_1m_2}(x-x_1)\) with this u directly get to answer..............
m1 is slope of given line = -2 m2 is slope between lines = tan 45 .............
|dw:1347997360648:dw|
im trying to work this out by finding out inclination angles for the two lines PR and PQ
since we have a point P(1, 2 ) already, we just need to find the inclination angle
|dw:1347997747693:dw|
nice hint @ganeshie8 , i have some idea now....
inclination angles easy to find.........
no this is roundabout way... im sure using ur formula we get to the answer much faste.r...
can someone just elucidate what or how I can solve the problem??
|dw:1347997933295:dw|
did u get that figure ? @robinfr93
|dw:1347998406604:dw| solved!
main thing was to find slope of one of the line = 3 using inclination angles....

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