OG13 DS 74
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
How to solve this Q?
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While solving coordinate geometry problems, specifically DS problems, try to draw the scenario and solve by visualizing possible situations.sanaa.rizwan 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
In this case, if you read the problem carefully or draw the given points on the coordinate plane, you'll notice that y-coordinates of the points are same. Now, the midpoint of the points is ((-3 + 1)/2, (-3 + -3)/2) = (-1, -3)
As the line segment joining the given two points is horizontal, all the points equidistant from these two points will lie on the vertical line passing through (-1, -3). In other words, all the points equidistant from these two points will have x-coordinate = -1 and y-coordinate will vary.
So, the question reduces to "In the xy coordinate plane, is the x-coordinate of the point R equal to -1?"
Now, we can clearly see statement 1 is sufficient but statement 2 is not.
The correct answer is A.
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Don't solve; DRAW.sanaa.rizwan wrote:OG13 DS 74
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
Statement 1: The x-coordinate of point R is -1.
In the words, R is on the line x = -1:
As the figure above shows, if R is at any point along x = -1, it will be equidistant between (-3,-3) and (1,-3).
SUFFICIENT.
Statement 2: Point R lies on the line y = -3
As the figure above shows:
If R is at (-1,-3), it will be equidistant between (-3,-3) and (1,-3).
If R is at (2,-3), it will NOT be equidistant between (-3,-3) and (1,-3).
INSUFFICIENT.
The correct answer is A.
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