Point (1,0) is closest to which of the following lines? A.

Question

Point (1,0) is closest to which of the following lines?

A. y = x
B. y = 1
C. y + x = 3
D. x = 2
E. x + y = −1

M24-34

bhushan252 · Accepted Answer

i hope now i m clear

walker · Answer

It is easier to draw the point and lines.

1) y=x - a half of the diagonal of 1*1 square: 1/\sqrt{2} 
2)y=1 - 1
3)y+x=3 - goes too far, definitely >1 
4)x=2 - 1
5)x+y=-1 - goes too far, definitely >1

bhushan252 · Answer

my approach is just visualize each line in mind 
( i know its easier said than done...but considering 2 mins time....i think this is the fastest way)
refer image attached.......Now the task is to find min distance from a line in options to the point (1,0).......this can also be done by a formula from a geometry chapter

First visualise point (1,0)...now to calculate min distance....here its very helpful to know a property.....in 45-45-90 triangle.....sides are in 1:1:srt(2) proportion....now apply this in following options

1) y=x....since y=x.....aangle of line wrto x axis = 45 ( shown in fig)....we need perpendicular distance hence another angle = 90 deg....thus it becomes a triangle of 45-45-90....hence hypoteneous is 1...now equate the proportion as 1:1:srt(2) = x:x:1.....this gives x = 1/srt(2)min distance = 1/srt(2)

2)y=1....min distance = 1
3)y+x=3......min distance = srt(2).......apply the same logic as of option 1
4)x=2.....min distance = 1
5)x+y=-1....min distance = srt(2).......apply the same logic as of option 1

OA A

mbaiseasy · Answer

Best approach is to sketch the lines.
Practice getting the y-intercept and the x-intercepts. 
These two intercepts will guide you win in sketching your lines.

1) (0,0) (1,1) (2,2) ... (n,n)
2) draw a line that intersects y=1  (This is quickly beaten by y=x. OUT!) 
3) (0,3) (3,0)  (This is quickly beaten by y=x. OUT!) 
4) draw a line that intersects x=2
5) (0,-1) (-1,0)  (This is quickly beaten by y=x. OUT!)

Looking at the scetch you will notice that (4) x=2 has a minimum distance of 1.
Looking at the scetch of (1) x=y has a minimum distance of d < 1

Bunuel · Answer

Look at the diagram below: https://gmatclub.com/forum/download/file.php?id=23422 As you can see point (1,0) is closest to line y = x. Answer: A. Untitled.png

AnuK2222 · Answer

Correct answer A,
used elimination to remove C and E, distance from options B and C is equal and we cannot have two correct answer. Leaves us with A by making a rough sketch to confirm.

MohdZaidKhan · Answer

do we et grid paper in the exam ?

Rickooreoisb · Answer

Between - A. y = x
B. y = 1

B will be far becasue I can draw a line from 1,0 meeting agt 0.5,0.5 which will be shorter distance

Point (1,0) is closest to which of the following lines? A.

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Point (1,0) is closest to which of the following lines? A.

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