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Coordinate Geometry!

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by Ozlemg » Mon Jul 11, 2011 1:05 am
In the rectangular coordinate system,are the points (r,s) and (u,v)
equidistant from the origin?
(1) r+s=1
(2) u=1-r;v=1-s;


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Source: — Data Sufficiency |
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by amit2k9 » Mon Jul 11, 2011 1:12 am
r^2 + s^2 = u^2 + v^2 ?

a no clue about u,v.hence not sufficient.

b r^2+s^2 = (1-r)^2 + (1-s)^2

= 1-2r+r^2+ 1-2s+s^2 = 2-2(r+s)+[r^2+s^2].

thus not equal. hence sufficient.

B it is.
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by Mom4MBA » Mon Jul 11, 2011 9:16 pm
In the rectangular coordinate system,are the points (r,s) and (u,v)
equidistant from the origin?
(1) r+s=1
(2) u=1-r;v=1-s;
for equidistance
√(r² + s²) = √(u² + s²)

statement 1: not sufficient as nothing is known about u and v

statement 2:
√(r² + s²) = √(u² + s²)
√(r² + s²) = √[(1-r)² + (1-s)²]
√(r² + s²) = √[2 + r² + s² -2(r+s)]

not of use

taking both the statements together:

√(r² + s²) = √[2 + r² + s² -2(r+s)]
√(r² + s²) = √[2 + r² + s² -2]
√(r² + s²) = √(r² + s²)

both together sufficient

Answer c
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