Need help on this coordinate geomeotry question

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Discussion Overview

The discussion revolves around a coordinate geometry question involving the identification of points on a circle defined by the equation x^2 + y^2 - 4x + 6y - 12 = 0. Participants are particularly focused on determining the labels of points A and B where the circle intersects the x-axis, specifically addressing the reasoning behind labeling one point as A and the other as B.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant found the intersection points of the circle with the x-axis to be (-2,0) and (6,0) but questioned the labeling of these points as A and B.
  • Another participant argued that the specific labels of A and B do not affect the calculation of the distance between them, emphasizing that distance is symmetric.
  • Further responses reiterated the idea that the labels are arbitrary and that the ordered pairs are what matter for the problem.
  • One participant suggested that the labeling might be based on the relative positions of the points on the x-axis, noting that (-2,0) is to the left of (6,0).
  • Another participant pointed out that the labeling is likely dictated by the problem statement, which specifies that A is (-2,0).

Areas of Agreement / Disagreement

Participants generally agree that the labels A and B are arbitrary and do not affect the distance calculation. However, there is disagreement regarding the significance of the labeling in the context of the problem, with some emphasizing the importance of the ordered pairs and others focusing on the labels themselves.

Contextual Notes

Some participants noted that the question's wording may provide specific instructions on labeling points, which could influence the discussion on the significance of the names assigned to the points.

9Vibes
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So here's how it goes.

Find the coordinates of the centre and the radius of the circle
x^2 + y^2 - 4x + 6y -12 =0

a)If the circle cuts the x-axis at the points A and B , find the length of line segment AB.

My question is , I have actually found 2 points , they are
(-2,0) and (6,0)

However , How do I know which point is A or which point is B?
in the answer sheet , (-2,0) is A , but can anyone explain why?
Why can't A be (6,0)?
 
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Are you serious? It doesn't matter! You are not asked to find A and B separately you are asked to find the distance between A and B. And the distance "from A to B" is the same as the distance "from B to A".:smile:
 
HallsofIvy said:
Are you serious? It doesn't matter! You are not asked to find A and B separately you are asked to find the distance between A and B. And the distance "from A to B" is the same as the distance "from B to A".:smile:

Yes , but right now I am asking why is A at (-2,0) and not at (6,0)?
For A is used in the later part B , I don't have the question with me now , so I can't really describe the part B of the question...
 
9Vibes said:
Yes , but right now I am asking why is A at (-2,0) and not at (6,0)?
For A is used in the later part B , I don't have the question with me now , so I can't really describe the part B of the question...

Recheck HallsOfIvy's answer again. The ordered pair values are important; not the name you gave the points. "A" and "B" are just names. The ordered pairs tell us WHERE each point is. You needed to find the ordered pairs, and you succeeded.
 
Its probably because the -2,0 point lies to the left (occurs before) of the 6,0 point. There's no particular reason to it.
 
9Vibes said:
Yes , but right now I am asking why is A at (-2,0) and not at (6,0)?
For A is used in the later part B , I don't have the question with me now , so I can't really describe the part B of the question...
Who says that "A is at (-2, 0)"? If that information in in the question, it is because you are told that A is (-2, 0) and they want you to label the point (-2, 0) and use that later in the problem.
 

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