intersecting lines

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hutch27: Master | Next Rank: 500 Posts; Posts: 141; Joined: Fri Sep 07, 2012 10:25 pmFollowed by: 1 member; Location: NY; Thanked: 5 times

by hutch27 » Sat May 11, 2013 2:28 pm

can two lines intersect each other if they are directly on top of eachother?

for example, if you have line segment A with points (1,3) and (2,2) [slope = -1]... can line B with slope -1 intersect line segment A ? In other words, can a line directly on top of a line segment intersect eachother, even though they dont have a point of intersection?

Even though we don't know the exact equation of line B, can we still conclude that it can never intersect line segment A since it can only fall on top of A?

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Source: Beat The GMAT — Quantitative Reasoning | Sat May 11, 2013 2:28 pm

Atekihcan: Master | Next Rank: 500 Posts; Posts: 149; Joined: Wed May 01, 2013 10:37 pmFollowed by: 9 members; Thanked: 54 times

by Atekihcan » Sun May 12, 2013 1:34 am

Generally the "never intersects" scenario is reserved for parallel lines with different y-intercepts.
But if two lines are identical, i.e. they coincides (or in you words : on top of each other), then they are the same lines and there should not be any concept of intersection as they are same. But in for the sake of mathematics, it is often said that the lines intersect at infinite number of points, i.e. they intersect at all points on the line.

Last edited by Atekihcan on Sun May 12, 2013 9:47 am, edited 1 time in total.

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hutch27: Master | Next Rank: 500 Posts; Posts: 141; Joined: Fri Sep 07, 2012 10:25 pmFollowed by: 1 member; Location: NY; Thanked: 5 times

by hutch27 » Sun May 12, 2013 8:09 am

I asked this because I saw a GMAT question from a test-prep company that was worded something like this

does line P intersect line segment AB [ Point A is (1,3) and B is (2,2) ]

1.) line P's slope is -1
2.) the equation of line P is y=-x+4

the Oa is b

but I thought the answer was D andfor those above reasons

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Jim@StratusPrep: MBA Admissions Consultant; Posts: 2279; Joined: Fri Nov 11, 2011 7:51 amFollowed by: 266 members; Location: New York; Thanked: 660 times; GMAT Score:770

by Jim@StratusPrep » Mon May 13, 2013 8:38 am

There should be something to distinguish that they cannot overlap. The reason it is not clear is because of the way the question is written here.

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