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Current Student D
Joined: 12 Aug 2015
Posts: 2562
Schools: Boston U '20 (M)
GRE 1: Q169 V154 A Straight Line is formed using two points A(3,3) and B(6,6) . Another  [#permalink]

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8 00:00

Difficulty:   55% (hard)

Question Stats: 62% (02:10) correct 38% (02:38) wrong based on 92 sessions

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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..!!

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 8023
Re: A Straight Line is formed using two points A(3,3) and B(6,6) . Another  [#permalink]

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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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Current Student D
Joined: 12 Aug 2015
Posts: 2562
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: A Straight Line is formed using two points A(3,3) and B(6,6) . Another  [#permalink]

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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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Math Expert V
Joined: 02 Aug 2009
Posts: 8023
Re: A Straight Line is formed using two points A(3,3) and B(6,6) . Another  [#permalink]

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

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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 [ 3.34 KiB | Viewed 1501 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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_________________ Re: A Straight Line is formed using two points A(3,3) and B(6,6) . Another   [#permalink] 30 Sep 2018, 15:47
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