Distances in the Coordinate Plane

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In the rectangular coordinate system above, point Q (not shown) is the same distance from the line y = x as point P, and it is the same distance from the y axis as point P is from the x axis. Point R (not shown) lies at both the same distance from the x axis and the same distance from the y axis as point Q, but is in a different location. If the coordinates of point P are (4,2), which of the following are possible coordinates of point R?

Review: Distances in the Coordinate Plane


Explanation

In this question, point P resides at the coordinates (4, 2). The not-shown point Q is "the same distance from the y axis as point P is from the x axis." That little phrase means that since point P has a y coordinate of 2, point Q will have an x coordinate of 2, and will thus be (2, ?). It will therefore have coordinates (2, 4), since it is equidistant from y = x. Finally, since point R is the same distance from each axis as point Q, it must have an x coordinate of and a y coordinate of .

The correct answer is (C).


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