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A, B, and C are three distinct points in the xy-coordinate  [#permalink]

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Question Stats: 68% (01:32) correct 32% (01:35) wrong based on 604 sessions

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A, B, and C are three distinct points in the xy-coordinate system, and line segment AB is either parallel to the x-axis or the y-axis. 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?  [#permalink]

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imerial wrote:
A, B, and C are three distinct points in the xy-coordinate system, and line segment AB is either parallel to the x-axis or the y-axis. 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?  [#permalink]

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imerial wrote:
A, B, and C are three distinct points in the xy-coordinate system, and line segment AB is either parallel to the x-axis or the y-axis. 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 || x-axis
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 || some-axis, 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?  [#permalink]

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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?  [#permalink]

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Good observation.
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GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37 Re: A, B, and C are three distinct points in the xy-coordinate  [#permalink]

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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 xy-coordinate  [#permalink]

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A, B, and C are three distinct points in the xy-coordinate system, and line segment AB is either parallel to the x-axis or the y-axis. 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 X-axis or Y-axis.
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 xy-coordinate  [#permalink]

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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 co-linear with A and B , hence a triangle can be formed . B is sufficient. Re: A, B, and C are three distinct points in the xy-coordinate   [#permalink] 15 Jan 2019, 08:25
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