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# In the rectangular coordinate system, are the points (a, b)

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Director
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In the rectangular coordinate system, are the points (a, b) [#permalink]

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15 Jul 2008, 18:51
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In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) sqrt(a^2) + sqrt(b^2) = sqrt(c^2) + sqrt(d^2)

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Current Student
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15 Jul 2008, 18:57
i think B makes sense to me..

basically says the distance of A and C is the same and so is B and D..

which means sqrt(a^2 + b^2)= sqrt(C^2 + d^2)

1) is insuff

a/b=c/d for instance a=6, b=3 c=12 d=6 they are not equidistant...but if a=b=c=d they are insuff..

2) |a|+|b|=|c|+|d|

now if |b|=o then |a|=|c|+|d|

i can also see when |b| is not equal to 0..

insuff...

together we know that |b| is not 0.. and infact |a|=|c| etc..

C it is.

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Director
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15 Jul 2008, 21:27
statement 1 : a/b = c/d take example 2,4 and 3,6 ... not suff

statement 2 : |a| + |b| = |c| + |d| take example 2,4 and 1,5 ... not suff

combine : a/b = c/d = k ---- (1)

|a| + |ka| = |c| + |kc|
(k+1) |a| = (k+1) |c|
|a| = |c|
from (1)
|b| = |d|

take any value for (a,b) = (3,6) the corresponding values of (c,d) will be (3,6)(-3,6)(-3,-6)(3,-6) ... in all cases the distance from (0,0) will be same .... Suff

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VP
Joined: 03 Apr 2007
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15 Jul 2008, 22:01
jimmyjamesdonkey wrote:
In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) sqrt(a^2) + sqrt(b^2) = sqrt(c^2) + sqrt(d^2)

C

distance = sqrt(a^2+b^2) = sqrt(c^2+d^2) =?

stat1 :NS
stat2 :NS

from 1 and 2 , a=c, b=d
sqrt(a^2+b^2) = sqrt(c^2+d^2)

suff

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Director
Joined: 14 Aug 2007
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16 Jul 2008, 05:56
goalsnr wrote:
jimmyjamesdonkey wrote:
In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) sqrt(a^2) + sqrt(b^2) = sqrt(c^2) + sqrt(d^2)

C

distance = sqrt(a^2+b^2) = sqrt(c^2+d^2) =?

stat1 :NS
stat2 :NS

from 1 and 2 , a=c, b=d
sqrt(a^2+b^2) = sqrt(c^2+d^2)

suff

How did u calculate the portion I have marked red above?

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SVP
Joined: 17 Jun 2008
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16 Jul 2008, 07:06
Stmt1: a/b = c/d or (a+b)/b = (c+d)/d

Stmt 2: a+b = c+d

Thus, from Stmt1 : b = d and consequently, a = c.

Thus, sqrt(a^2+b^2) = sqrt(c^2+d^2)

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Re: MGMAT: DS Coordinates   [#permalink] 16 Jul 2008, 07:06
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