M12-20

Question

Which of the following points is closest to the line  y = x ?

A. (2, -1)
B. (2, 4)
C. (-1, 1)
D. (2, 1)
E. (-2, 0)

Bunuel · Answer

Official Solution:

Which of the following points is closest to the line  y = x ?

A. (2, -1)
B. (2, 4)
C. (-1, 1)
D. (2, 1)
E. (-2, 0)

Note that while Geometry is not tested on GMAT Focus, coordinate geometry is tested under the Functions and Graphing sections found in the Official Guide for GMAT Focus Edition.
 
Arguably, the easiest way to evaluate this is by making a sketch and checking each of the answer choices visually. Refer to the diagram below:
 
 https://gmatclub.com/gmat-practice-tests/resources/import/img/m12-20.png 
 
As you can see, the point (2, 1) is the closest to the line  y = x .

Answer: D

toby001 · Answer

Hi Banuel,

I understand the solution, but I was wondering if there's an algebraic approach to this problem.

Thanks.

HARRY113 · Answer

Hi toby001, This can be solved algebraically, but it will consume a lot of your time. I feel this approach is most appropriate for GMAT, since you would be given a scratch paper, which is having graph available. You just need to plot the co-ordinates...

Coming to your question. Find the line perpendicular and that passes through the points in options. Once you get the line again solve for distance between the line and point of interception of both lines. The following is the formula to find the distance from a point to the line. The distance from a point (m, n) to the line Ax + By + C = 0 is given by: d = {∣Am+Bn+C∣}/ {\sqrt{(A^2 + B^2}} +1 Kudos. If found helpful Cheers, Harry

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

M12-20

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