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..

- anonymous

- jamiebookeater

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- anonymous

Draw a picture first. it always helps visualize

- anonymous

Well there wasn't one but neway heres what I can do..

- anonymous

When it says right angled at (2,1) I think at that point it is 90 deg

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## More answers

- anonymous

|dw:1347994216890:dw|

- anonymous

yes dats pretty obvious isn't it??

- 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

yup, both the angles will be 45 degrees, i.e, 45+45+90

- anonymous

well ChmE??

- anonymous

well @ChmE

- anonymous

Can't anybody solve this??

- bahrom7893

Ok let me try.

- 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

just find points Q and R, given that we know P

- TuringTest

then use point slope and all that business

- anonymous

Its an isosceles right angled triangle that means 2 of its angle are 45 degrees and one is at 90 degrees..

- anonymous

@TuringTest the question is HOW???

- TuringTest

let's draw a bigger pic

- bahrom7893

|dw:1347994331965:dw|

- anonymous

btw the answers ae PQ = x+3y -5 and PR = 3x-y-5

- bahrom7893

lol does that help?

- anonymous

@bahrom7893 No dude!!!
Its already in the question...
:P

- TuringTest

|dw:1347994441088:dw|

- anonymous

Yeah now what??

- anonymous

I got it so far!!!
next step will be what??

- TuringTest

at x=2 what is y ?

- TuringTest

calm down dude I am explaining...

- anonymous

:P
Sorry its just that its getting in my head bad!!

- anonymous

well all that is given in the ques, no additionally details are provided..

- TuringTest

though I must admit I;m not sure exactly what they are asking
the equation for the pair? what do they mean?

- anonymous

hahhahahahah..
Exactly what Ive stumbled upon..

- anonymous

by pair of lines they mean PQ and PR

- TuringTest

but infinitely I assume, not a finite line segment....

- anonymous

nope its finite alright!!!

- TuringTest

then the answer must give bounds to x and y

- 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

|dw:1347994766490:dw|

- TuringTest

yeah that may help me understand what they are asking

- 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

PR*

- TuringTest

oh I misinterpreted the problem I see

- TuringTest

|dw:1347994998473:dw|so my assumption that the legs of the triangle followed the grid was wrong

- anonymous

@TuringTest Still don't get...

- 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

:P
well it isn't
@hartnn DUDE!!!
You were saying u got it ryt??
Will you do the honor of telling me how??

- hartnn

even i thought that lines are vertical and horizontal.....but they r not.....even i m stuck...

- hartnn

that seems the formula for tan(A+B) ....in the solution u mentioned....do u have some standard formulas in this topic ?

- anonymous

I know!!!
just one , but I don't understand hw to implement it in this one..

- anonymous

Two lines will be perpendicular to each other if...coeff of x^2 + coeff of y^2 = 0

- anonymous

but this is a first degreeequation so can't really put that in...

- hartnn

yes, that won't help..

- anonymous

Think people THINK!!!!
The person who can solve this will be titled a born genius..
:P

- TuringTest

|dw:1347995522447:dw|

- TuringTest

I dunno I'll have to drop this for now...

- anonymous

NOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!!
:'(

- hartnn

|dw:1347995617810:dw|
i don't know what i m doing......

- hartnn

6 equations 8 unknowns.

- anonymous

:P

- hartnn

mM=-1--->7th equation.

- hartnn

1 more equation and we are done.

- anonymous

you mean one more equation if was provided??

- hartnn

1 more equation WE need to find.

- anonymous

Take all the time you need, Ill be here for a while....

- hartnn

lol, very big equation it is!!
PQ=PR and distance formula :P

- anonymous

:P

- hartnn

we getting 8 equations and 8 unknowns
but its almost impossible to solve them simultaneously.....there must be another way...

- 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

and even how y-2 and x-2 ??
y-2 and x-1 maybe.....

- hartnn

we can use help of @ganeshie8 here....

- anonymous

Is he any good??

- hartnn

you will see.

- 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

m1 is slope of given line = -2
m2 is slope between lines = tan 45 .............

- ganeshie8

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- ganeshie8

im trying to work this out by finding out inclination angles for the two lines PR and PQ

- ganeshie8

since we have a point P(1, 2 ) already, we just need to find the inclination angle

- ganeshie8

|dw:1347997747693:dw|

- hartnn

nice hint @ganeshie8 , i have some idea now....

- hartnn

inclination angles easy to find.........

- ganeshie8

no this is roundabout way... im sure using ur formula we get to the answer much faste.r...

- anonymous

can someone just elucidate what or how I can solve the problem??

- hartnn

|dw:1347997933295:dw|

- hartnn

did u get that figure ? @robinfr93

- hartnn

|dw:1347998406604:dw|
solved!

- hartnn

main thing was to find slope of one of the line = 3 using inclination angles....

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