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Which pair of points could both appear on the same line, if that line Updated on: 01 Oct 2023, 05:49
Originally posted by nechets on 27 Dec 2013, 15:51.
Last edited by BottomJee on 01 Oct 2023, 05:49, edited 4 times in total.
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Col (A): (-6, 5)
Col (B): (8, -3)
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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.

Show SpoilerOE:
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

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Col (A) Col (B) Values
(-7, -4)
(-6, 5)
(0, -3)
(4, 0)
(8, -3)
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Col (A): (-6, 5)
Col (B): (8, -3)
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Which pair of points could both appear on the same line, if that line 27 Dec 2013, 19:49
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nechets
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)

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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
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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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Which pair of points could both appear on the same line, if that line 27 Feb 2014, 12:33
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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!

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