geometry query

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advita: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Sep 13, 2010 8:06 pm; Thanked: 2 times

by advita » Wed Jan 26, 2011 12:11 am

hi guys/experts,

i have 1 query regarding geometry.

>i know if line are // then they are not intersecting each other.

if i say - we choose a line segment say CD (in between line AB). then can we say line AB is intersecting line segment CD.

for example, if i say the eqn of line AB: y-x=-1. Q: does line AB intersect the line segment having coordinate C(1,2) D(3,4).??

Q2:
related to the same Q1: what does intersection means.??
(// line have zero angle - no intersection).... what about overlapping lines..?? are they intersecting each others.??

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Source: Beat The GMAT — Problem Solving | Wed Jan 26, 2011 12:11 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Jan 26, 2011 12:24 am

advita wrote:if i say - we choose a line segment say CD (in between line AB). then can we say line AB is intersecting line segment CD.

What do you mean by "a line segment say CD (in between line AB)"?
If you mean to say, a line segment CD on the line AB, i.e. basically CD is a part of line AB, then they intersect at infinite number of points.

advita wrote:for example, if i say the eqn of line AB: y-x=-1. Q: does line AB intersect the line segment having coordinate C(1,2) D(3,4).??

The equation of AB is y = x - 1, whereas equation for CD is y = x + 1
As their slopes are equal, they are parallel to each other.

advita wrote:what does intersection means.??
(// line have zero angle - no intersection).... what about overlapping lines..?? are they intersecting each others.??

Intersection means crosses or touches each other.
For any two lines A and B, there are three possible cases,

1. A and B coincides on each other ----> They intersect at infinite numbers of points
2. A and B are parallel to each other -----> No intersection
3. A and B has none of the above relation --> They intersect at only one point

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advita: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Sep 13, 2010 8:06 pm; Thanked: 2 times

by advita » Wed Jan 26, 2011 12:38 am

GREAT...this is simply great.
Thanks for clarification.

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