Which of the following points is closest to line \(y=x?\)
A. \((2, 1)\)
B. \((2, 4)\)
C. \((1, 1)\)
D. \((2, 1)\)
E. \((2, 0)\)
Answer: D
Source: GMAT Club Tests
Which of the following points is closest to line \(y=x?\)
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Solution:Gmat_mission wrote: ↑Wed Sep 23, 2020 5:43 amWhich of the following points is closest to line \(y=x?\)
A. \((2, 1)\)
B. \((2, 4)\)
C. \((1, 1)\)
D. \((2, 1)\)
E. \((2, 0)\)
Answer: D
Source: GMAT Club Tests
The best way to solve this problem is to draw the graph:
Clearly, we see that (2, 1) is closest to the line y = x.
Alternate Solution:
Every ordered pair (x, y) on the line y = x has the difference y  x as 0. For example, the ordered pair (6, 6) is on the line y = x, and the difference y  x = 6  6 = 0.
For the given ordered pairs, the point with the smallest difference of y  x will be closest to the line y = x. We see that the point (2, 1) has a difference of 1  2 = 1 = 1, and all the other ordered pairs have differences whose absolute values are greater than 1.
Answer: D
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