## robinfr93 Group Title 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.. one year ago one year ago

1. ChmE Group Title

Draw a picture first. it always helps visualize

2. robinfr93 Group Title

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

3. ChmE Group Title

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

4. robinfr93 Group Title

|dw:1347994216890:dw|

5. robinfr93 Group Title

yes dats pretty obvious isn't it??

6. ChmE Group Title

Right angle isoceles means that the sides to each side of the right angle are equal. Ya I'd say so after the picture.

7. robinfr93 Group Title

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

8. robinfr93 Group Title

well ChmE??

9. robinfr93 Group Title

well @ChmE

10. robinfr93 Group Title

Can't anybody solve this??

11. bahrom7893 Group Title

Ok let me try.

12. bahrom7893 Group Title

I want to say PQ is just x=2 and PR is just y=1, but what if the triangle is at an angle..

13. TuringTest Group Title

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

14. TuringTest Group Title

then use point slope and all that business

15. robinfr93 Group Title

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

16. robinfr93 Group Title

@TuringTest the question is HOW???

17. TuringTest Group Title

let's draw a bigger pic

18. bahrom7893 Group Title

|dw:1347994331965:dw|

19. robinfr93 Group Title

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

20. bahrom7893 Group Title

lol does that help?

21. robinfr93 Group Title

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

22. TuringTest Group Title

|dw:1347994441088:dw|

23. robinfr93 Group Title

Yeah now what??

24. robinfr93 Group Title

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

25. TuringTest Group Title

at x=2 what is y ?

26. TuringTest Group Title

calm down dude I am explaining...

27. robinfr93 Group Title

28. robinfr93 Group Title

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

29. TuringTest Group Title

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

30. robinfr93 Group Title

hahhahahahah.. Exactly what Ive stumbled upon..

31. robinfr93 Group Title

by pair of lines they mean PQ and PR

32. TuringTest Group Title

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

33. robinfr93 Group Title

nope its finite alright!!!

34. TuringTest Group Title

then the answer must give bounds to x and y

35. robinfr93 Group Title

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...

36. TuringTest Group Title

|dw:1347994766490:dw|

37. TuringTest Group Title

yeah that may help me understand what they are asking

38. robinfr93 Group Title

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...

39. robinfr93 Group Title

PR*

40. TuringTest Group Title

oh I misinterpreted the problem I see

41. TuringTest Group Title

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

42. robinfr93 Group Title

@TuringTest Still don't get...

43. TuringTest Group Title

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

44. robinfr93 Group Title

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

45. hartnn Group Title

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

46. hartnn Group Title

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

47. robinfr93 Group Title

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

48. robinfr93 Group Title

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

49. robinfr93 Group Title

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

50. hartnn Group Title

yes, that won't help..

51. robinfr93 Group Title

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

52. TuringTest Group Title

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53. TuringTest Group Title

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

54. robinfr93 Group Title

NOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!! :'(

55. hartnn Group Title

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

56. hartnn Group Title

6 equations 8 unknowns.

57. robinfr93 Group Title

:P

58. hartnn Group Title

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

59. hartnn Group Title

1 more equation and we are done.

60. robinfr93 Group Title

you mean one more equation if was provided??

61. hartnn Group Title

1 more equation WE need to find.

62. robinfr93 Group Title

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

63. hartnn Group Title

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

64. robinfr93 Group Title

:P

65. hartnn Group Title

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

66. robinfr93 Group Title

I typed in the equation and the solution that was given in the text.. The only questions bugging my mind is Y and HOW??

67. hartnn Group Title

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

68. hartnn Group Title

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

69. robinfr93 Group Title

Is he any good??

70. hartnn Group Title

you will see.

71. hartnn Group Title

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..............

72. hartnn Group Title

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

73. ganeshie8 Group Title

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74. ganeshie8 Group Title

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

75. ganeshie8 Group Title

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

76. ganeshie8 Group Title

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77. hartnn Group Title

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

78. hartnn Group Title

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

79. ganeshie8 Group Title

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

80. robinfr93 Group Title

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

81. hartnn Group Title

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82. hartnn Group Title

did u get that figure ? @robinfr93

83. hartnn Group Title

|dw:1347998406604:dw| solved!

84. hartnn Group Title

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