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Which pair of points could both appear on the same line [#permalink]

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27 Dec 2013, 15:51

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.

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.

Re: Which pair of points could both appear on the same line [#permalink]

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27 Dec 2013, 19:49

1

This post received KUDOS

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.

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.

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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