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ds coordinate geometry

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Director
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ds coordinate geometry [#permalink] New post 21 Mar 2006, 08:51
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In the xy plane, does the line with equation y = 3x + 2 contain the point (r,s)?

1) (3r + 2 - s)(4r+ 9 - s) = 0
2) (4r - 6 - s) 93r + 2 - s) = 0

Please explain your ans .
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 [#permalink] New post 21 Mar 2006, 10:46
In the xy plane, does the line with equation y = 3x + 2 contain the point (r,s)?

1) (3r + 2 - s)(4r+ 9 - s) = 0
2) (4r - 6 - s) (3r + 2 - s) = 0

The math here is slightly complicated -- almost too complicated to do in two minutes to ensure that you have the correct answer.

The question can be restated as: Is s = 3r + 2

Statement 1:

12r^2 + 35r - 7rs - 11s + s^2 + 18 = 0

Now, we can relate r to s using the original equation, y = 3x + 2, by plugging in those variables

s = 3r + 2

If the equation can be resolved to this, then we have an answer. Let's solve for s
12r^2 + 35r - 7rs - 11s + s^2 + 18

s^2 - (11 + 7r)s = -12r^2 - 35r - 18

At this point, we can't solve for s (at least I'm 99% sure that we can't -- unless someone can show me another way).

Inconclusive, so we have to go to statement 2

Statement 2:

12r^2 - 10r - 7rs + 4s + s^2 -12 = 0
We run into the same problem here, so inconclusive

Statements 1 & 2:
12r^2 + 35r - 7rs - 11s + s^2 + 18 = 12r^2 - 10r - 7rs + 4s + s^2 -12

Which equals:

45r - 15s + 30 = 0

15s = 45r + 30
Therefore, s = 3r+2

Answer C
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 [#permalink] New post 21 Mar 2006, 14:21
Do we really have to go through that lengthy procedure?

stmt1:
1) (3r + 2 - s)(4r+ 9 - s) = 0
->s = 3r+2 or s= 4r+9
In suff

stmt2:
2) (4r - 6 - s) 93r + 2 - s) = 0
s= 3r+2 or s= 4r-6
Insuff

Combining both
s has a common value s= 3r+2

So C
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 [#permalink] New post 21 Mar 2006, 14:29
Much better way to solve. Good call.
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 [#permalink] New post 21 Mar 2006, 18:51
Nayan wrote:
Do we really have to go through that lengthy procedure?

stmt1:
1) (3r + 2 - s)(4r+ 9 - s) = 0
->s = 3r+2 or s= 4r+9
In suff

stmt2:
2) (4r - 6 - s) 93r + 2 - s) = 0
s= 3r+2 or s= 4r-6
Insuff

Combining both
s has a common value s= 3r+2

So C


I understand how you got s = 3r + 2.. but what I dont understand is that why having 3r + 2 in both the equations makes the answer C..
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  [#permalink] 21 Mar 2006, 18:51
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