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A, B, and C are three distinct points in the xycoordinate
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22 Aug 2011, 12:18
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A, B, and C are three distinct points in the xycoordinate system, and line segment AB is either parallel to the xaxis or the yaxis. Do the points A, B, and C form the vertices of a triangle? (1) The coordinates of point A are (4, 2). (2) The coordinates of point B are (8, 2), and those of point C are (5, 7).
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Re: Is ABC a triangle?
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22 Aug 2011, 12:55
imerial wrote: A, B, and C are three distinct points in the xycoordinate system, and line segment AB is either parallel to the xaxis or the yaxis. Do the points A, B, and C form the vertices of a triangle?
(1) The coordinates of point A are (4, 2).
(2) The coordinates of point B are (8, 2), and those of point C are (5, 7). Basically they will only not form a triangle if they all have the same x coordinate or the same y coordinate. (1) we are only given one point so it may form a triangle or may for a straight line. In (2) we can see that A and B have neither the same X or same Y coordinate, thus any other point on the grid will form a triangle with these two points. B



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Re: Is ABC a triangle?
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22 Aug 2011, 13:32
imerial wrote: A, B, and C are three distinct points in the xycoordinate system, and line segment AB is either parallel to the xaxis or the yaxis. Do the points A, B, and C form the vertices of a triangle?
(1) The coordinates of point A are (4, 2).
(2) The coordinates of point B are (8, 2), and those of point C are (5, 7). (1) A=(4,2); For the sake of simplicity, let's say B=(5,2) That makes AB  xaxis Now, C can be (6,2). ABC will form a straight line, not triangle. Or, C can be (10,10). ABC will form a triangle because the three points are NOT collinear. Not Sufficient. (2) B=(8,2) AND C=(5,7) Because we are told that AB  someaxis, A must lie either on line y=2 OR x=8 considering B=(8,2) AND also A can't be (8,2) itself, for all the three points are distinct. Thus, ABC can not be collinear AND will always be a triangle irrespective of the coordinates A may have. Sufficient. See the pic: Attachment:
AB_Parallel_To_Axis.JPG [ 31.36 KiB  Viewed 6334 times ]
Ans: "B"
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Re: Is ABC a triangle?
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22 Aug 2011, 13:39
Just a side note: If "distinct" wasn't used in the question, C would have been the answer.!
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Re: Is ABC a triangle?
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03 Nov 2011, 11:03
Good observation.



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Re: A, B, and C are three distinct points in the xycoordinate
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19 Dec 2015, 23:50
any point that lies on the line x=8 would not be collinear with a point on (5,7) and (8,2) at the same time. Hence, Statement 2 is sufficient to prove that the three points are not on the same line. Two points are anyways always collinear. Hence B
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Re: A, B, and C are three distinct points in the xycoordinate
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04 Sep 2018, 17:33
A, B, and C are three distinct points in the xycoordinate system, and line segment AB is either parallel to the xaxis or the yaxis. Do the points A, B, and C form the vertices of a triangle?
(1) The coordinates of point A are (4, 2).
(2) The coordinates of point B are (8, 2), and those of point C are (5, 7).
Ans B.
Statement 1: A(4, 2) and we know AB is parallel to either Xaxis or Yaxis. Let's say B could be either (4, y) or (x, 2), where x and y are variables. No info about C, so insufficient
Statement2: B(8, 2), so A could be either (8, y) or (x, 2), where x and y are variables. C is given as (5, 7). Clearly sufficient (regardless of the value of x and y).
Regards, S.R



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Re: A, B, and C are three distinct points in the xycoordinate
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15 Jan 2019, 08:25
We need coordinates for three points . Points A and B are parallel to either x or y axis , so if we get one point we can pretty much predict the other point
ex if pt A i s (2,3) then a point B on either x axis or y axis will make the line AB parallel to x axis or the y axis
so line passing through (2,3) and (2,0) is parallel to x axis and line passing through (0,3) is parallel to y axis .
1) Does not give any information about the points B and C so not sufficient.
2. Coordinates of Points B and C are given we know that coordinates of Point A are such that line passing through points AB is either parallel to X axis or Y axis . if it is parallel to y axis it would have the same x coordinate , if it is parallel to the xaxis it would have the same Y coordinate
hence points can be A, B, C can be ( 8,4) , (8,2), (5,7) C is not colinear with A and B , hence a triangle can be formed . B is sufficient.




Re: A, B, and C are three distinct points in the xycoordinate
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15 Jan 2019, 08:25






