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

[Gmat_mission]

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

[Scott@TargetTestPrep]

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

Solution:

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