## butterflyprincess 3 years ago Major MATH HELP! D: ** Pic included!

1. butterflyprincess

2. butterflyprincess

Help? :(

3. STEPHEN1998

wat

4. butterflyprincess

I need some help with this problem

5. STEPHEN1998

ok

6. STEPHEN1998

7. butterflyprincess

I dont have onne, I need help :| I attached a link of the problem

8. STEPHEN1998

i did

9. STEPHEN1998

hold on

10. butterflyprincess

thnx (:

11. zordoloom

Do you still need help?

12. butterflyprincess

13. STEPHEN1998

ya

14. zordoloom

Okay, Do you know how to even start working on this problem?

15. butterflyprincess

No :C

16. zordoloom

So are you working with vectors?

17. butterflyprincess

indeed I am!

18. butterflyprincess

Im just tottally lost on this problem

19. zordoloom

Ok, so have you done vector proofs before?

20. butterflyprincess

no neverO=

21. zordoloom

ok, so ob+ba=oa

22. zordoloom

0=(0,0) A=(x1,y1) B=(x2,y2)

23. zordoloom

Vector BA=A-B=(x1-x2, y1-y2)

24. butterflyprincess

okk

25. zordoloom

Good so far?

26. zordoloom

All what you have to do now is find vecotor OA and vecotr OB

27. butterflyprincess

O: oh really but is there like another pic you have to draw/

28. zordoloom

no

29. butterflyprincess

oh cool

30. zordoloom

|dw:1352869007184:dw|

31. zordoloom

so vector BA is equal to A-B so when you subtract the points element-wise you get x1-x2 and y1-y2

32. zordoloom

|dw:1352869116355:dw|

33. butterflyprincess

Oh right, now I find Oa Ob ?How can I do thta again?

34. zordoloom

|dw:1352869175679:dw|

35. zordoloom

now you do the same for vector ob

36. zordoloom

|dw:1352869297947:dw|

37. butterflyprincess

So OB is OB = O-B= <0-x2 , 0-y2 > ?

38. zordoloom

no, it would be <OB> = B-O = <x2,y2>

39. zordoloom

So, now you need to subtract <OB> from <OA>. to prove that it equals <AB>

40. butterflyprincess

ohhh right!

41. zordoloom

42. zordoloom

look at the attachment, the circled ones.

43. zordoloom

How would you prove the?

44. zordoloom

*them?

45. zordoloom

They are equal.

46. zordoloom

so, by the subtraction of the vectors, you prove that <BA> = <OA>-<OB>

47. butterflyprincess

OH theyre equal!! Its < x1-x2 , y1-y2 > !

48. zordoloom

pretty much.

49. zordoloom

Now to solve part 2, set point c equal to (x3, y3)

50. zordoloom

then I would solve for x3,y3 in terms of the other known quantities, x1,y1 and x2,y2 using the given ratio. the rest is just algebra.

51. butterflyprincess

So all what xOA is saying is to ditribute the x?

52. zordoloom

Ya

53. butterflyprincess

Oh okay yy

54. butterflyprincess

|dw:1352870110521:dw|

55. butterflyprincess

right?

56. zordoloom

yes.

57. butterflyprincess

Cool thanks ((:

58. hartnn

<OC>=C-O

59. hartnn

<BC>/<CA> =x/y so, (C-B)/(A-C) =x/y now can, you isolate C from here ? try it...

60. butterflyprincess

you want me to isolare c from (C-B)/(A-C) =x/y right?

61. hartnn

yes,

62. hartnn

u see, how i got, (C-B)/(A-C) =x/y from given condition, <BC>/<CA> =x/y

63. butterflyprincess

Wait how would you do that because C is being subtracted

64. hartnn

u mean how to isolate C ? cross-multiply....

65. butterflyprincess

yea youd get y(c-b) = x(a-c) ...

66. hartnn

try to isolate C from that...

67. butterflyprincess

so I distribute..first then

68. butterflyprincess

yc-cb = xa - xc

69. hartnn

yes, distribute then bring all terms with 'c' together, then factor out c

70. hartnn

its yc-yb on the left...

71. butterflyprincess

So C= xa-xc / (y-b)

72. hartnn

there, u were not able to isolate C, notice, c is there on right side also

73. hartnn

yc-yb = xa - xc yc+xc = xa+yb got this step ?

74. hartnn

now can u isolate c ?

75. butterflyprincess

I thought ititd be yc-cb = xa - xc since u cross mult tho..

76. butterflyprincess

|dw:1352871594989:dw|

77. hartnn

|dw:1352871643318:dw|

78. butterflyprincess

right x)

79. hartnn

|dw:1352871704757:dw|

80. butterflyprincess

yesyes i did that xD

81. hartnn

what does left side simplify to ?

82. hartnn

knowing that its given that x+y=1

83. butterflyprincess

C= xa+yb / y+x

84. hartnn

what is x+y= ?

85. butterflyprincess

Wait but does C equal to that O:

86. hartnn

yes.

87. butterflyprincess

oh okay lol Um y+x = .. ?

88. hartnn

its given to be =1 see the question

89. butterflyprincess

Oh cool so it would just be xa+yb

90. hartnn

yes, c=xa+yb now u know what to do next ?

91. butterflyprincess

PLug it to...

92. hartnn

we know that C=(x3,y3) and O=(0,0) so can you find <OC> = ?

93. butterflyprincess

<x3-0,y3-0>

94. hartnn

which is ?

95. butterflyprincess

x3,y3

96. hartnn

so <OC> =C so we can replace C by <OC> right ?

97. butterflyprincess

ohhyeauhhh! ool!

98. hartnn

in same way, we can replace A by ... ? B by ... ?

99. butterflyprincess

A with x1,y1??

100. hartnn

A with <OA>

101. hartnn

<OC> =C so we can replace C by <OC> <OA> =A so we can replace A by <OA> <OB> =B so we can replace B by <OB> right ?

102. butterflyprincess

yes..

103. hartnn

so put all those in c=xa+y and see whether u get what needs to be proven..

104. butterflyprincess

|dw:1352872625517:dw|

105. butterflyprincess

Do u mean plug in the value sliket his

106. hartnn

|dw:1352872688272:dw|

107. butterflyprincess

OH THATS what you ment I tots get that!

108. hartnn

all steps clear ? any doubts ?

109. butterflyprincess

Wait and how did u kno that OC=c and OA =A and OB = B ?

110. hartnn

C = (x3,y3) <OC> =C-O = (x3,y3)-(0,0) = (x3-0,y3-0) = (x3,y3) = C same for A and b

111. hartnn

got it ?

112. butterflyprincess

yea thanks (: Do you think we can do another in like 10 min?? I I need to sleep asap since I need to wake up early tomorrow (x

113. hartnn

same type ? ....actually even i need to go in few minutes...

114. hartnn

lets me see the question atleast

115. butterflyprincess

OK but && Oh and alsoo how did you know that ( C- B)/(A-C) = x/y

116. hartnn

it is given that BC /CA = x/y now BC=C-B CA=A-C

117. hartnn

remember for any vector XY, we can write it as Y-X

118. butterflyprincess

oh okay why is it flipped again?

119. hartnn

flipped again ? means ?

120. butterflyprincess

Oh I mean like why isnt it like BC= B-c instead its C-B

121. hartnn

its the conventional way of representation, but if you take BC=B-C , you will get same exact final answer....

122. hartnn

so its no difference, just a way of representation

123. butterflyprincess

Oh right k thnx! lemme post the other problem I dont think we have enough tim :C