GMAT OFFICIAL GUIDE DS – In the xy-coordinate plane…

Solution:

We are given points (-3,-3) and (1,-3), and we need to determine whether point R is equidistant from these points. Since the line segment connecting these two points is parallel to the x-axis, we can determine that a point that is equidistant from points (-3,-3) and
(1,-3) would be anywhere on the line x = -1. Thus, if we can determine that the
x-coordinate of point R is -1 (i.e., anywhere on the line x = -1), we will know that point R is equidistant from points (-3,-3) and (1,-3). Let’s illustrate this below.

Statement One Alone:

The x-coordinate of point R is -1.

Since the x coordinate of point R is -1, point R is located somewhere on the line x = -1 and is therefore equidistant from points (-3,-3) and (1,-3). Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

Point R lies on the line y = -3.

This means the y-coordinate of R is -3. However, knowing only the y-coordinate of point R is not enough to determine whether point R is equidistant from points (-3,-3) and (1,-3).  For example, if R = (-1, -3), then R is equidistant from (-3,-3) and (1,-3). On the other hand, if R = (0, -3), then R is closer to (1, -3) than it is to (-3, -3). Statement two is not sufficient to answer the question.