Need help on this coordinate geomeotry question

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In summary, the question asks for the coordinates of the center and radius of a circle given by the equation x^2 + y^2 - 4x + 6y - 12 = 0. The length of line segment AB, where A and B are points on the x-axis where the circle intersects, is also asked to be found. The points (-2, 0) and (6, 0) are found to be the points of intersection, but it does not matter which point is labeled as A or B since the distance from A to B is the same as the distance from B to A. The ordered pairs are important in identifying the points, not the names given to them.
  • #1
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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  • #2
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:
 
  • #3
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...
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 

1. What is coordinate geometry?

Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes and figures using a coordinate system. This system uses a set of numbers or coordinates to identify the position of points on a graph.

2. How do I solve a coordinate geometry question?

To solve a coordinate geometry question, you need to first identify the given coordinates and plot them on a graph. Then, use basic geometric principles such as distance formula, slope formula, and midpoint formula to find the required information.

3. What are the common formulas used in coordinate geometry?

The most common formulas used in coordinate geometry include the distance formula, slope formula, midpoint formula, and equation of a line (point-slope form, slope-intercept form, and standard form).

4. What are some real-life applications of coordinate geometry?

Coordinate geometry has numerous real-life applications, such as in navigation systems, mapping, computer graphics, architecture, and engineering. It is also used in physics and science to study the motion of objects and their trajectories.

5. Can I use a calculator to solve coordinate geometry questions?

Yes, you can use a calculator to solve coordinate geometry questions. However, it is important to understand the underlying concepts and formulas to ensure accurate results. Some calculators also have specific functions and modes for coordinate geometry problems.

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