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A Straight Line is formed using two points A(3,3) and B(6,6) . Another

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A Straight Line is formed using two points A(3,3) and B(6,6) . Another  [#permalink]

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New post 02 Apr 2016, 15:36
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A Straight Line is formed using two points A(3,3) and B(6,6) . Another point P(x,y) lies between A and B such that AP/BP = 10 . The coordinates of P are =>

[A] (5,5)
[B] ( 61/11,61/11)
[C] (63/11,63/11)
[D] (36/11,36/11)
[E] (58/11,58/11)

Try this Out ..!
Give me a correct solution with explanation..!!

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Re: A Straight Line is formed using two points A(3,3) and B(6,6) . Another  [#permalink]

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New post 02 Apr 2016, 19:42
1
Chiragjordan wrote:
A Straight Line is formed using two points A(3,3) and B(6,6) . Another point P(x,y) lies between A and B such that AP/BP = 10 . The coordinates of P are =>

[A] (5,5)
(B) ( 61/11,61/11)
[C] (63/11,63/11)
[D] (36/11,36/11)
[E] (58/11,58/11)

Try this Out ..!
Give me a correct solution with explanation..!!


Hi Chiragjordan,

Good Q

the line is basically angle bisector of x axis in 1st quadrant..

P point divides AB in 10:1 portion..
since x and y are similar, we may do away with first finding the length of AB and then dividing in into ratio of 10:1 and then again convert that into coordinates..


so P lies at 10 distance away if AB is divided in 11 parts so AP = (6-3) *10/11 =30/11..
But A is at 3, so P will be at 30/11 + 3 = (30+33)/11 = 63/11
so coord of (x,y) are (63/11,63/11)
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: A Straight Line is formed using two points A(3,3) and B(6,6) . Another  [#permalink]

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New post 02 Apr 2016, 19:48
1
chetan2u wrote:
Chiragjordan wrote:
A Straight Line is formed using two points A(3,3) and B(6,6) . Another point P(x,y) lies between A and B such that AP/BP = 10 . The coordinates of P are =>

[A] (5,5)
(B) ( 61/11,61/11)
[C] (63/11,63/11)
[D] (36/11,36/11)
[E] (58/11,58/11)

Try this Out ..!
Give me a correct solution with explanation..!!


Hi Chiragjordan,

Good Q

the line is basically angle bisector of x axis in 1st quadrant..

P point divides AB in 10:1 portion..
since x and y are similar, we may do away with first finding the length of AB and then dividing in into ratio of 10:1 and then again convert that into coordinates..


so P lies at 10 distance away if AB is divided in 11 parts so AP = (6-3) *10/11 =30/11..
But A is at 3, so P will be at 30/11 + 3 = (30+33)/11 = 63/11
so coord of (x,y) are (63/11,63/11)


Nice ..
I actually used the ratio formula => P(x,y)=(K1x2+K2x1)/ (K1+K2), (K1y2+K2y1)/(K1+K2) here x1,y1 and x2 ,y2 are coordinates of A,B
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Re: A Straight Line is formed using two points A(3,3) and B(6,6) . Another  [#permalink]

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New post 02 Apr 2016, 19:55
Chiragjordan wrote:
chetan2u wrote:
Chiragjordan wrote:
A Straight Line is formed using two points A(3,3) and B(6,6) . Another point P(x,y) lies between A and B such that AP/BP = 10 . The coordinates of P are =>

[A] (5,5)
(B) ( 61/11,61/11)
[C] (63/11,63/11)
[D] (36/11,36/11)
[E] (58/11,58/11)

Try this Out ..!
Give me a correct solution with explanation..!!


Hi Chiragjordan,

Good Q

the line is basically angle bisector of x axis in 1st quadrant..

P point divides AB in 10:1 portion..
since x and y are similar, we may do away with first finding the length of AB and then dividing in into ratio of 10:1 and then again convert that into coordinates..


so P lies at 10 distance away if AB is divided in 11 parts so AP = (6-3) *10/11 =30/11..
But A is at 3, so P will be at 30/11 + 3 = (30+33)/11 = 63/11
so coord of (x,y) are (63/11,63/11)


Nice ..
I actually used the ratio formula => P(x,y)=(K1x2+K2x1)/ (K1+K2), (K1y2+K2y1)/(K1+K2) here x1,y1 and x2 ,y2 are coordinates of A,B


You are correct in your approach--
Using this you can find any coordinates if you know the ratio in which it divides the line...
If you look closely this formula is nothing BUT the weighted average method which one uses in MIXTURE..
Two ends are given and their distance( Quantity in case of mixtures) is given .. we are finding the average through that
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: A Straight Line is formed using two points A(3,3) and B(6,6) . Another  [#permalink]

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New post 03 Apr 2016, 04:39
2
Chiragjordan wrote:
A Straight Line is formed using two points A(3,3) and B(6,6) . Another point P(x,y) lies between A and B such that AP/BP = 10 . The coordinates of P are =>

[A] (5,5)
( 61/11,61/11)
[C] (63/11,63/11)
[D] (36/11,36/11)
[E] (58/11,58/11)

Try this Out ..!
Give me a correct solution with explanation..!!


Attachment:
Line.png
Line.png [ 3.34 KiB | Viewed 1366 times ]


x = {1(3) + 10(6)}/(1 + 10) => 63/11
y = {1(3) + 10(6)}/(1 + 10) => 63/11

[b]Thus the correct answer is (C)
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Re: A Straight Line is formed using two points A(3,3) and B(6,6) . Another  [#permalink]

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New post 30 Sep 2018, 14:47
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Re: A Straight Line is formed using two points A(3,3) and B(6,6) . Another &nbs [#permalink] 30 Sep 2018, 14:47
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