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

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

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