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Which pair of points could both appear on the same line

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Joined: 04 Oct 2013
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Which pair of points could both appear on the same line [#permalink] New post 27 Dec 2013, 14:51
Which pair of points could both appear on the same line, if that line passes through the origin? Please make one selection in each column, with column A containing the point with the lesser x-value and column B containing the point with the greater x-value.

Col (A) Col (B)
( ) ( ) (-7, -4)

( ) ( ) (-6, 5)

( ) ( ) (0, -3)

( ) ( ) (4, 0)

( ) ( ) (8, -3)

[Reveal] Spoiler:
MY Question: I wonder if the two points chosen should have the same slope. What do you guys think?

OE:
For a line to pass through the origin, there are really four options for the quadrants it can pass through. It can pass through quadrants I and III; it can pass through II and IV; it can pass directly through the x-axis; and it can pass directly through the y-axis. Point (-7, -4) is in quadrant III, and there isn't a matching quadrant I to go with it. Point (0, -3) is on the y-axis, and there isn't another point on the y-axis to match it. Similar for point (4, 0) which is on the x-axis with no pairing. Point (-6, 5) is in quadrant II and point (8, -3) is in quadrant III, so these two points could be on the same line that passes through the origin.


Source: VeritasPrep

Last edited by nechets on 29 Dec 2013, 05:01, edited 1 time in total.
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Re: Which pair of points could both appear on the same line [#permalink] New post 27 Dec 2013, 18:49
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nechets wrote:
Which pair of points could both appear on the same line, if that line passes through the origin? Please make one selection in each column, with column A containing the point with the lesser x-value and column B containing the point with the greater x-value.

Col (A) Col (B)
( ) ( ) (-7, -4)

( ) ( ) (-6, 5)

( ) ( ) (0, -3)

( ) ( ) (4, 0)

( ) ( ) (8, -3)

[Reveal] Spoiler:
MY Question: I wonder if the two points choosed should have the same slope. What do you guys think?

OE:
For a line to pass through the origin, there are really four options for the quadrants it can pass through. It can pass through quadrants I and III; it can pass through II and IV; it can pass directly through the x-axis; and it can pass directly through the y-axis. Point (-7, -4) is in quadrant III, and there isn't a matching quadrant I to go with it. Point (0, -3) is on the y-axis, and there isn't another point on the y-axis to match it. Similar for point (4, 0) which is on the x-axis with no pairing. Point (-6, 5) is in quadrant II and point (8, -3) is in quadrant III, so these two points could be on the same line that passes through the origin.


Source: VeritasPrep



This looks liked a bad question to me. I agree with you that the both points chosen should have the same slope to the origin. Interestingly, their answer of (-6, 5) and (8, -3) have different slopes to the origin... meaning if you draw a line between these two points, it will not pass through the origin.
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Re: Which pair of points could both appear on the same line [#permalink] New post 27 Feb 2014, 11:33
What exactly is the answer? are there 3 answers instead of 2? (8,-3) (-6,5) (0,-3) ?

I thought the question was asking which 2 of the points cross the origin if both of the points were on the same line. Someone please explain.

Thanks!
Re: Which pair of points could both appear on the same line   [#permalink] 27 Feb 2014, 11:33
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