Rectangular Coordinate System - Data Sufficiency - The Beat The GMAT Forum

Rectangular Coordinate System - Data Sufficiency

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arbiter: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Mon Jun 09, 2008 9:17 am; Thanked: 2 times

by arbiter » Sat Aug 22, 2009 8:47 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 and v=1-s

OA is C

Can anyone of you explain the concepts here.

arbiter

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Source: Beat The GMAT — Problem Solving | Sat Aug 22, 2009 8:47 am

kaulnikhil: Master | Next Rank: 500 Posts; Posts: 338; Joined: Fri Apr 17, 2009 1:49 amFollowed by: 3 members; Thanked: 9 times

by kaulnikhil » Sat Aug 22, 2009 9:08 am

distance of r and s from center r^2 + s^2
distance of u and v u^2 + v^2
1...not sufficient ..no u and v present
2....squaring both sides
we get u ^2 = 1+r^2 -2r
V^2 = 1 +s^2 -2s

add them up
u^2 + V^2 = 2 + r^2 + s^2 -2r -2s

clearly not sufficient
put r = 1-s from 1
we get r^2 + S^2 = u^2 +v^2
hence C

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