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Coordinate Geometry - 1

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shivanigs: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Fri Apr 27, 2012 5:10 am; Followed by:2 members

Coordinate Geometry - 1

by shivanigs » Fri Aug 24, 2012 2:20 am

Hi,

Request help with the following question.Thanks..

Request you to please refer to the attached image.

What are the coordinates of S?

A)OS slope = 1/3
B)ST slope = 1/2

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Image.doc: (19.5 KiB) Downloaded 127 times

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Source: Beat The GMAT — Data Sufficiency | Fri Aug 24, 2012 2:20 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Fri Aug 24, 2012 3:06 am

assume the co-ordinates of S are (x,y).
considering each option alone:
1) given: slope of OS = 1/3 and co-ordinates of O and T are (0,0)and(5,0) respectively.
OS slope is 1/3
slope of line when given two points(m) = (y1 - y2)/(x1 - x2)
so, we will get the line equation of OS. the point can be any point on the line.
so with the option 1, we can`t get the exact point.
2) given: slope of ST = 1/2 and co-ordinates of O and T are (0,0)and(5,0) respectively.
we will get the line equation of ST.
so with the option 2 also, we can`t get the exact point.
combining 1 and 2, we have two different lines (as their slopes are different), they will meet at exactly one point.
hence, it can be answered using both the options

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prat_agl: Senior | Next Rank: 100 Posts; Posts: 63; Joined: Tue Apr 06, 2010 10:01 pm; Thanked: 4 times; Followed by:1 members

by prat_agl » Fri Aug 24, 2012 6:38 am

A- can get the equation of OS as we know the slope and a point (origin), but this will not give the value of S. Insufficient.
b - Can get the equation of ST as we know the slope and a point (5,0) but this will not give the value of S. Insufficient.

Combining both, we have equation of two lines and we need to find the point of intersection of these 2 line. Sufficient.

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Ankur87: Master | Next Rank: 500 Posts; Posts: 110; Joined: Sun Aug 19, 2012 4:39 am; Thanked: 9 times; GMAT Score:640

by Ankur87 » Fri Aug 24, 2012 10:03 am

Anurag@Gurome wrote:assume the co-ordinates of S are (x,y).
considering each option alone:
1) given: slope of OS = 1/3 and co-ordinates of O and T are (0,0)and(5,0) respectively.
OS slope is 1/3
slope of line when given two points(m) = (y1 - y2)/(x1 - x2)
so, we will get the line equation of OS. the point can be any point on the line.
so with the option 1, we can`t get the exact point.
2) given: slope of ST = 1/2 and co-ordinates of O and T are (0,0)and(5,0) respectively.
we will get the line equation of ST.
so with the option 2 also, we can`t get the exact point.
combining 1 and 2, we have two different lines (as their slopes are different), they will meet at exactly one point.
hence, it can be answered using both the options

hello sir,
i didn't get this solution,
i mean if we are having o(0,0) and s(x,y)
and slope of OS is 1/3 then y2-y1/x2-x1 = 1/3
i.e y2-0/x2-0 = 1/3
y2/x2 = 1/3
y2 = 1, x2 = 3.

same with the line ST.

please correct me where am i wrong.

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by Anurag@Gurome » Mon Aug 27, 2012 9:38 pm

Hi ankur,
when y2/x2 = 1/3,
it does not mean y2 = 1 and x2 = 3. it can be any set of values that satisfy the ratio 1/3.
for example
when y2 = 2, x2 = 6
when y2 = 0.5, x2 = 1.5
we will have infinite set of values satisfying this condition