[email protected] wrote:In the xy coordinate plane, is point R equidistant from points (-3,-3) and (1,-3)?

1) The x coordinate of point R is -1
2) Point R lies on the line y= -3

Target question: Is point R equidistant from points (-3,-3) and (1,-3)?

This question is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

First sketch the two given points


Notice that the point (-1, -3) is equidistant from the two given points. MORE IMPORTANTLY, every point on the line x = -1 is equidistant from the two given points.


So, we can rephrase the target question . . .
Rephrased target question: Is point R on the line x = -1?

Statement 1: The x coordinate of point R is -1
If the x-coordinate is -1, then point R is definitely on the line x = -1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Point R lies on the line y= -3
This tells us nothing about whether or not point R is on the line x = -1?
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

[email protected] wrote: ↑

Fri Aug 02, 2013 8:16 am

In the xy coordinate plane, is point R equidistant from points (-3,-3) and (1,-3)?

1) The x coordinate of point R is -1
2) Point R lies on the line y= -3

Solution:

Question Stem Analysis:

We need to determine whether point R is equidistant from points (-3,-3) and (1,-3), If it is, then it must be on the perpendicular bisector of the segment connecting (-3,-3) and (1,-3). Since the segment connecting (-3,-3) and (1,-3) is horizontal, the perpendicular bisector of the segment must be vertical, passing through the midpoint of the segment. Since the midpoint of the segment is (-1, -3), the equation of the perpendicular bisector is x = -1. That is, if R is any point on the line x = -1, then it’s equidistant from points (-3,-3) and (1,-3).

Statement One Alone:

Since the x-coordinate of point R is -1, R must be a point on the line x = -1. Therefore, it is equidistant from points (-3,-3) and (1,-3). Statement one alone is sufficient.

Statement Two Alone:

We see that R is a point on the line containing the segment connecting (-3,-3) and (1,-3). However, we can’t determine whether it is equidistant from points (-3,-3) and (1,-3). For example, if R = (-1, -3), i.e., the midpoint of (-3,-3) and (1,-3), then it is equidistant from points (-3,-3) and (1,-3). Otherwise, it is not. Statement two alone is not sufficient.

Answer: A