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

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

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15 Nov 2008, 15:56
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In a 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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15 Nov 2008, 16:37
tarek99 wrote:
In a rectangular coordinate system, are the points (a,b) and (c,d) equidistant from the origin?

(1) $$(a/b) = (c/d)$$

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

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

2 says a+b = c+d means$$a^2 + b ^2 + 2ab = c^2+d^2 +2cd$$

Insufficient

Together with ad=bc and a+b = c+d cannot arrive at $$sqrt (a^2+b^2) = sqrt (c^2+d^2) or a^2 + b ^2= c^2+d^2$$

E
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15 Nov 2008, 21:20
tarek99 wrote:
In a rectangular coordinate system, are the points (a,b) and (c,d) equidistant from the origin?

(1) $$(a/b) = (c/d)$$
(2) $$sqrt(a^2) + sqrt(b^2) = sqrt(c^2) + sqrt(d^2)$$

My intution says C.

Cuz if a/b = c/d and $$sqrt(a^2) + sqrt(b^2) = sqrt(c^2) + sqrt(d^2)$$, either a or b = either c or d.

Does anybody has any example where they are not equal?
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15 Nov 2008, 23:17
i think E is the ans.

v cannot take them proportionate or equal if we are not given values..
values can be anything...like

1+ 3 = 2 + 2..

pls enlighten..
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16 Nov 2008, 00:46
bindrakaran001 wrote:
i think E is the ans.

v cannot take them proportionate or equal if we are not given values..
values can be anything...like

1+ 3 = 2 + 2..

pls enlighten..

how do you make the ratio equal?
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16 Nov 2008, 21:28
icandy wrote:
tarek99 wrote:
In a rectangular coordinate system, are the points (a,b) and (c,d) equidistant from the origin?

(1) $$(a/b) = (c/d)$$

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

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

2 says a+b = c+d means$$a^2 + b ^2 + 2ab = c^2+d^2 +2cd$$

Insufficient

Together with ad=bc and a+b = c+d cannot arrive at $$sqrt (a^2+b^2) = sqrt (c^2+d^2) or a^2 + b ^2= c^2+d^2$$

E

Agree with E with exact same reasoning
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16 Nov 2008, 21:36
icandy wrote:
tarek99 wrote:
In a rectangular coordinate system, are the points (a,b) and (c,d) equidistant from the origin?

(1) $$(a/b) = (c/d)$$

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

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

2 says a+b = c+d means$$a^2 + b ^2 + 2ab = c^2+d^2 +2cd$$

Insufficient

Together with ad=bc and a+b = c+d cannot arrive at $$sqrt (a^2+b^2) = sqrt (c^2+d^2) or a^2 + b ^2= c^2+d^2$$

E

I think it is C
Continuing from where you left
a/b = c/d
a/b +1 = c/d +1
a+b/b = c+d/d
since a+b = c+d
b = d, similaryly a = c
So, yes they are equidistant
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16 Nov 2008, 23:48
LiveStronger wrote:
icandy wrote:
tarek99 wrote:
In a rectangular coordinate system, are the points (a,b) and (c,d) equidistant from the origin?

(1) $$(a/b) = (c/d)$$

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

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

2 says a+b = c+d means$$a^2 + b ^2 + 2ab = c^2+d^2 +2cd$$

Insufficient

Together with ad=bc and a+b = c+d cannot arrive at $$sqrt (a^2+b^2) = sqrt (c^2+d^2) or a^2 + b ^2= c^2+d^2$$

E

I think it is C
Continuing from where you left
a/b = c/d
a/b +1 = c/d +1
a+b/b = c+d/d
since a+b = c+d
b = d, similaryly a = c
So, yes they are equidistant

You are correct! I am with C now...
Lesson learnt: do not leave calculation in between!!!

By the way , a/b +1 = c/d +1 this was bit tricky.
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17 Nov 2008, 08:37
I think that there is even a better way of looking at this problem. First of all, let's start with statement 1:

(1) ratios can never determine the exact values. They might both be equal or they might not be. For example:

1/2 = 5/10

They are both the same ratio, but they are not necessarily the same value. So not suff.

(2) The different numbers that we can use is really infinite here. For example:

5 + 5 = 10 or

9 + 1 = 10 and I can just come up with MANY other different combination

(1&2)

when both the ratios of a/b and c/d are the same and the sum of a & b is the same as that of c & d, then they both have equal value.

Therefore C
Re: DS: Coordinate   [#permalink] 17 Nov 2008, 08:37
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