## robinfr93 3 years ago 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..

1. ChmE

Draw a picture first. it always helps visualize

2. robinfr93

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

3. ChmE

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

4. robinfr93

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5. robinfr93

yes dats pretty obvious isn't it??

6. ChmE

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

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

8. robinfr93

well ChmE??

9. robinfr93

well @ChmE

10. robinfr93

Can't anybody solve this??

11. bahrom7893

Ok let me try.

12. 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..

13. TuringTest

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

14. TuringTest

then use point slope and all that business

15. robinfr93

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

16. robinfr93

@TuringTest the question is HOW???

17. TuringTest

let's draw a bigger pic

18. bahrom7893

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19. robinfr93

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

20. bahrom7893

lol does that help?

21. robinfr93

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

22. TuringTest

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23. robinfr93

Yeah now what??

24. robinfr93

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

25. TuringTest

at x=2 what is y ?

26. TuringTest

calm down dude I am explaining...

27. robinfr93

28. robinfr93

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

29. TuringTest

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

30. robinfr93

hahhahahahah.. Exactly what Ive stumbled upon..

31. robinfr93

by pair of lines they mean PQ and PR

32. TuringTest

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

33. robinfr93

nope its finite alright!!!

34. TuringTest

then the answer must give bounds to x and y

35. robinfr93

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

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37. TuringTest

yeah that may help me understand what they are asking

38. robinfr93

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

PR*

40. TuringTest

oh I misinterpreted the problem I see

41. TuringTest

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

42. robinfr93

@TuringTest Still don't get...

43. 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

44. robinfr93

: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

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

46. hartnn

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

47. robinfr93

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

48. robinfr93

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

49. robinfr93

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

50. hartnn

yes, that won't help..

51. robinfr93

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

52. TuringTest

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53. TuringTest

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

54. robinfr93

NOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!! :'(

55. hartnn

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

56. hartnn

6 equations 8 unknowns.

57. robinfr93

:P

58. hartnn

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

59. hartnn

1 more equation and we are done.

60. robinfr93

you mean one more equation if was provided??

61. hartnn

1 more equation WE need to find.

62. robinfr93

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

63. hartnn

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

64. robinfr93

:P

65. hartnn

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

66. robinfr93

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

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

68. hartnn

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

69. robinfr93

Is he any good??

70. hartnn

you will see.

71. 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..............

72. hartnn

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

73. ganeshie8

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74. ganeshie8

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

75. ganeshie8

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

76. ganeshie8

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77. hartnn

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

78. hartnn

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

79. ganeshie8

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

80. robinfr93

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

81. hartnn

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82. hartnn

did u get that figure ? @robinfr93

83. hartnn

|dw:1347998406604:dw| solved!

84. hartnn

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