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In the standard (x,y) coordinate plane, a straight line segment is dra

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Bunuel
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In the standard (x,y) coordinate plane, a straight line segment is dra [#permalink] New post   15 Jan 2021, 03:15
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In the standard (x,y) coordinate plane, a straight line segment is drawn to connect (0,0) and (4,4). Which of the following sets of points, when connected by a straight line segment, will intersect the original segment?

(A) (–3,3) and (3,4)
(B) (0,–1) and (4,3)
(C) (0,1) and (4,5)
(D) (1,0) and (8,4)
(E) (2,1) and (2,5)
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Re: In the standard (x,y) coordinate plane, a straight line segment is dra [#permalink] New post   15 Jan 2021, 03:39
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The first line segment has slope of 1.So any line segment that intersects it cannot have a slope of 1. So lines B and C are ruled out.

Among remaining 3 options, A has slope - 1/6,D has slope 4/7 and E has infinite slope, i.e. parallel to the y axis.

For point E, since we know that x value will remain constant at 2, we see that it will cross the point (2,2) so it will intersect the first line.

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In the standard (x,y) coordinate plane, a straight line segment is dra [#permalink] New post   Updated on: 06 Feb 2021, 10:59
As far as my rational goes, due to the diction "will intersect the original segment", only Option E gets us the correct value of (2,1), where the line segment meets the original, however its slope is undefined (parallel to Y-Axis).

Option A & D implies that those line segments will have positive slopes but they don't cut across the original segment.
And solving Option B & C fetches us slope of 1 identical to original line segment.

So Its option E.

Please correct my reasoning if got wrong.

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Shubham

Originally posted by ShubhamA on 31 Jan 2021, 08:43.
Last edited by ShubhamA on 06 Feb 2021, 10:59, edited 1 time in total.
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Re: In the standard (x,y) coordinate plane, a straight line segment is dra [#permalink] New post   06 Feb 2021, 08:22
I am not able to eliminate option A, please help
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Re: In the standard (x,y) coordinate plane, a straight line segment is dra [#permalink] New post   10 Feb 2021, 08:51
bond001 wrote:
I am not able to eliminate option A, please help


Option A is incorrect as line segment formed by joining those co-ordinates wont intersect the original line segment { formed by (0,0) & (4,4) }, though it will cut across if you extend it further.

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Re: In the standard (x,y) coordinate plane, a straight line segment is dra [#permalink] New post   29 Jun 2022, 23:50
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Re: In the standard (x,y) coordinate plane, a straight line segment is dra [#permalink]
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