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

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22 Aug 2011, 11:18

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35% (medium)

Question Stats:

68% (02:07) correct
32% (01:23) wrong based on 225 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).

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

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 2719 times ]

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

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19 Dec 2015, 22:50

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 xy-coordinate
[#permalink]
19 Dec 2015, 22:50

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