Point dividing a line segment (externally)

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Discussion Overview

The discussion revolves around the concept of dividing a line segment externally, particularly how a point can divide a line segment when it lies outside the segment. Participants seek intuitive explanations and clarity on the definitions and implications of external division in geometry.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in understanding how a point can divide a line externally, requesting a simple intuitive explanation.
  • Another participant emphasizes the need for a precise definition of what it means to divide a line externally.
  • A participant attempts to clarify the concept by explaining that a point dividing a line segment can create ratios based on its position relative to the endpoints of the segment.
  • There is a discussion about the meaning of "join of two points," with one participant inferring that it refers to the line segment between two points.
  • One participant provides an example using real numbers to illustrate how a point outside the segment can create a ratio, questioning if this aligns with the textbook definition.
  • A later reply acknowledges understanding of the concept after initially struggling with the idea of external division, indicating a shift in comprehension regarding the nature of ratios when points lie outside the segment.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the clarity of the concept, with some expressing confusion and others attempting to clarify. Multiple interpretations of external division remain, and the discussion reflects varying levels of understanding.

Contextual Notes

There are indications that some participants may be struggling with language barriers or translation issues, which could affect their understanding of the mathematical concepts being discussed.

kashan123999
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I am just not able to connect this concept with my mind,i mean how is it possible to divide a line externally when the point is beyond the line..can anyone explain it intuitively in simple terms kindly? I am not able to grasp it clearly
 
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You need a precise definition.
divide a line externally
 
mathman said:
You need a precise definition.

no,actually I need an intuitive look into the concept maybe...
 
kashan123999 said:
no,actually I need an intuitive look into the concept maybe...

What mathman is saying:
It's not clear what your original post means. If you want some guidance, being more precise will help.
 
economicsnerd said:
What mathman is saying:
It's not clear what your original post means. If you want some guidance, being more precise will help.

I think i was quite precise sir...
There is an idea in my textbook regarding "point dividing a join of two points in a given ratio" so there in it is written if the point which divides the join of two points,lies beyond the join say AB...then it actually divides the points in ratios "externally"...i could not grasp this idea i mean how is it possible that a line divides in ratio externally
 
kashan123999 said:
I think i was quite precise sir...
There is an idea in my textbook regarding "point dividing a join of two points in a given ratio" so there in it is written if the point which divides the join of two points,lies beyond the join say AB...then it actually divides the points in ratios "externally"...i could not grasp this idea i mean how is it possible that a line divides in ratio externally
This is not at all clear, possibly as a result of being translated to English from some other language.

I think I understand part of it - "point dividing a join of two points in a given ratio". I infer that "join of two points" in your book means the line segment between the two points. If we call the two points A and B, we can call this line segment AB. If P is a point on this line segment, it divides the line segment into two parts that are in some ratio. For example, if P is located at 1/3 of the distance from A to B, then the ratio of AP to PB is 1:2 or 1/2.

With regard to the part about external ratios, I can only guess as to what is meant. For simplicity, let's assume that the points are on the real line, with A at 1 and B at 3. So the line segment AB lies between 1 and 3. If P is at 4, then |AP| = 3 and |PB| = 1. So the ratio of the two line segments is 3:1, and P is a point that is external to AB. Is this anywhere close to what your book is talking about?
 
Mark44 said:
This is not at all clear, possibly as a result of being translated to English from some other language.
I think I understand part of it - "point dividing a join of two points in a given ratio". I infer that "join of two points" in your book means the line segment between the two points. If we call the two points A and B, we can call this line segment AB. If P is a point on this line segment, it divides the line segment into two parts that are in some ratio. For example, if P is located at 1/3 of the distance from A to B, then the ratio of AP to PB is 1:2 or 1/2.
With regard to the part about external ratios, I can only guess as to what is meant. For simplicity, let's assume that the points are on the real line, with A at 1 and B at 3. So the line segment AB lies between 1 and 3. If P is at 4, then |AP| = 3 and |PB| = 1. So the ratio of the two line segments is 3:1, and P is a point that is external to AB. Is this anywhere close to what your book is talking about?

Yes thanks this is what i was talking About,i couldn't grasp that concept of having a ratio when the point which is dividing the line lies at,say in your case,4 on real line...kindly help me through it
 
What part of my explanation did you not understand?
 
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Actually in my book it talks about external ratio of the same line (AB in your case) and the point which divides them in some ratio k:k, lies beyond that line..I couldn't grasp it how it is an "external" ratio,i mean that would make it completely different (TO me IMHO and i an dumb TBH),it would sense like ratio b/w line AP and BP...and not like the ratio b/w A(a point) and B(same point)...BUT...wait..aah now i got that...thank you btw :) i got the idea of having ratio of the line...i was actually focusing more on "dividing thing" and was constantly thinking that it is only possible when the point which divides them lies "only" b/w them..now i got that.. thank you mate :)
 

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