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

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In the rectangular coordinate system, are the points (a, b) [#permalink] New post 23 Aug 2007, 12:51
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A
B
C
D
E

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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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Re: DS Coordinate Plane [#permalink] New post 23 Aug 2007, 13:57
Piter 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)


I think it is E.
as take any points

1;2 and then 2;1 those points are quidistant from the origin 0
or take -1;2 and -2;1 and those as well. so 1 is not suff.

2. the same thing only sum of the coordinates. a+b=c+d which is not sufficient to say yes or no

so E
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 [#permalink] New post 23 Aug 2007, 14:29
OA NOT E :wink:
OA and explanations later...
It's horrible problem...
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 [#permalink] New post 24 Aug 2007, 06:43
OA C
Quote:
To find the distance from the origin, we simply take the square root of the sum of the squared x- and y-coordinates, i.e. SQRT(x^+y^2).

(1) INSUFFICIENT: This simply tells us that the proportions between the x- and y-coordinates of both points are the same. E.g. take a = 5, b = 10, c = 6 and d = 12. The proportions are the same but the coordinate points are not the same distance from the origin. Conversely, if a = 5, b = 10, c = -5 and d = -10, then the proportions are equal and the coordinate points are the same distance from the origin.

(2) INSUFFICIENT: By simplifying the expression, we get |a| + |b| = |c| + |d|. This is not enough to tell if the points are equidistant. E.g. take a = 11, b = 1, c = 6 and d = 6. The expression |a| + |b| = |c| + |d| is true but the coordinate points are not the same distance from the origin. Conversely, if a = -6, b = 6, c = 6 and d = 6, then the given expression is true and the coordinate points are the same distance from the origin.

(1) AND (2) SUFFICIENT: Together the statements are sufficient. Why? If we know the proportion of a to b is the same as c to d and that |a| + |b| = |c| + |d|, then it must be the case that |a| = |c| and |b| = |d|. Plugging this into our distance formula, we get:

SQRT(a^+b^2) = SQRT(c^+d^2) ; Plug in |a| = |c| and |b| = |d| to get:
SQRT(a^+b^2) = SQRT(a^+b^2)

This is enough to show that the two points are equidistant.

The correct answer is C.
  [#permalink] 24 Aug 2007, 06:43
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