Need help on this coordinate geomeotry question

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The discussion revolves around finding the coordinates of the center and radius of a circle defined by the equation x^2 + y^2 - 4x + 6y - 12 = 0, and determining the points where it intersects the x-axis. The points found are (-2,0) and (6,0), but there is confusion regarding which point is labeled A and which is B. It is clarified that the labels A and B are arbitrary and do not affect the calculation of the distance between the two points. The important aspect is that the ordered pairs indicate their positions on the coordinate plane, with (-2,0) being to the left of (6,0). Ultimately, the naming of the points is less significant than their coordinates in solving the problem.
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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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