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if u want to do this question by elimination see x=1 and y =1 give the same answers , so both gets eliminated ..ofcourse A is the ans ..
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" What [i] do is not beyond anybody else's competence"- warren buffett My Gmat experience -http://gmatclub.com/forum/gmat-710-q-47-v-41-tips-for-non-natives-107086.html

i got the ANSWER by drawing the lines in a sheet and then finding out...is there any other easier way plz... i want to lessen the number of calculations i do...help required from the SMEs here
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Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

for x = 1 , the distance is 1 , so with y =1 so both of these are not answers and rest two line equations except y=x are far from the point (1,0). so left with option y=x.

may need to calculate the distance in other examples.

when the equation is y=1 then why is your line on the graph passing through y=2... also when we have x=2... the distance between y=x line and dst between x=2 line are same. i am confused badly.
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Hope to clear it this time!! GMAT 1: 540 Preparing again

when the equation is y=1 then why is your line on the graph passing through y=2... also when we have x=2... the distance between y=x line and dst between x=2 line are same. i am confused badly.

Hi,

The question asks out of all the lines in the option A to E, Which is closest to Point (1,0).

To your query:

Yes, the line should pass through Y=1. The distance between the point (1,0) and line Y=X and between Point (1,0) and line X=2 can be same so this tells you surely these 2 options are not the answers. You can eliminate these answer choices

Also Distance of Point (x1,y1) from a line \(ax+by+c=0\) can be found using the formulae

Refer to the figure below. Pt(1,0) is closest to Blue line which is y=x and hence ans is A. The distance from line x=2 is more as can be seen in the graph.

Attachments

m 1.png [ 11.39 KiB | Viewed 2739 times ]

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when the equation is y=1 then why is your line on the graph passing through y=2... also when we have x=2... the distance between y=x line and dst between x=2 line are same. i am confused badly.

Here is how i did this Question without using the Distance formula

After drawing all the lines We can see tht there is a close call between (A) \(y = x\) (B) \(y = 1\) (D) \(x = 2\)

Rest 2 could be eliminated just by seeing that their distance would be greater than the above 3 lines.

As for (B) \(y = 1\) (D) \(x = 2\)

Both have Perpendicular Distance =1 from the point \((1, 0)\) Now we can guess that since we have to find the shortest distance & no 2 options can have the minimum value & be the answer Thus \(y = x\) will be the answer