distance on the coordinate plane

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mehrasa: Master | Next Rank: 500 Posts; Posts: 279; Joined: Fri Nov 05, 2010 5:43 pmFollowed by: 1 member; Thanked: 15 times

by mehrasa » Mon Sep 12, 2011 9:28 pm

Is point A closer to point(1,2)than to point(2,1)?

1. Point A lies on the line y=x
2. Point A lies on the line y=-x

i am not sure about the answer choice, but i know (2,1) and (1,2) are two points reflected based on y=x then the distance between A and each of these points are the same. then stat I is sufficient
however about stat II, I think it is insufficient because for each place of point A the answer will be different...

to me A can be a good choice... what is ur idea?

Source: Beat The GMAT — Problem Solving | Mon Sep 12, 2011 9:28 pm

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Sep 12, 2011 10:07 pm

Yup [A] IMO too.

could have P(x,y) where x and y are of same value but opp signs. Whenever you interchange the sign, you get contradictory answers, so using you cannot say

mehrasa wrote:Is point A closer to point(1,2)than to point(2,1)?

1. Point A lies on the line y=x
2. Point A lies on the line y=-x

i am not sure about the answer choice, but i know (2,1) and (1,2) are two points reflected based on y=x then the distance between A and each of these points are the same. then stat I is sufficient
however about stat II, I think it is insufficient because for each place of point A the answer will be different...

to me A can be a good choice... what is ur idea?

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Mon Sep 12, 2011 10:09 pm

(1,2) and (2,1) -> reflected on y=x.
a) A lies on y=x. thus equidistant. Sufficient
b) A lies on y=-x. if we take (0,0) -> equidistant,
if we take (1,-1), distance from (1,2) = 3 and distance from (2,1) = root(5) <3.
Thus farther from (1,2).
if we take (-2,2), distance from (2,1) = root(17) and distance from (1,2) = 3
root(17)>3 thus nearer to (1,2)
insufficient
IMO A

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Tue Sep 13, 2011 5:41 am

If you draw a graph for y=x, you will see that any point on the line is equidistant from both points (1,2) and (2,1). Sufficient

Statement 2 is not sufficient as we cannot say which point would be closer to point A on line y=-x

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