Such as line segment AB

JulianMathHelp said:
Okay, so I did some thinking, when they say "what else can you construct when given a line segment such as AB" it is asking what other constructions can we create when we are given a segment such as AB, and by saying such as AB, it is implying that we should use AB as the given segment in the scenario correct? If they didn't say "such as AB", then the problem would be pretty hard to answer as you wouldn't really know which segment to start off on, and there would literally be an infinite amount of answers. Also, in the problem, it is given that the circles were constructed first, with equal radius, and the points are assumed as the center. This is my understanding. Also, sorry for leaving out some important details, it won't happen again, and im sincerely sorry for wasting your time :(.
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I am basing my interpretation on the first post. It doesn't say the circles were constructed first. If the first post does not contain the full text of the problem, it would be very helpful to correct it, so we are finally on the same page.
If it is given that the circles have equal radius and the center of one lies on the other circle, it would be equivalent to constructing them on a segment as in the diagram.
 
ok, so now that we’re on the same page, because the question says ..such as segment AB, is it implying for me to use AB as the given segment in the problem?
 
JulianMathHelp said:
ok, so now that we’re on the same page, because the question says ..such as segment AB, is it implying for me to use AB as the given segment in the problem?
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I don't know whether we are on the same page since you haven't posted the full problem.
It was absolutely clear from the beginning that you should use AB as the given segment. I don't know why you brought up other hypothetical segments.
 
lev888 said:
I don't know whether we are on the same page since you haven't posted the full problem.
It was absolutely clear from the beginning that you should use AB as the given segment. I don't know why you brought up other hypothetical segments.
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But wasn't the full problem given in post #12?
JulianMathHelp said:
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The literal wording of the problem is: What else can this diagram help you construct when given a line segment such as AB¯? Share your ideas with the class.
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I think it is clear that they are saying you are given segment AB, then you construct the two circles, then you ... what?

@JulianMathHelp, you haven't answered my questions in post #15. Can you see things you could construct from the diagram?
 
Dr.Peterson said:
But wasn't the full problem given in post #12?

I think it is clear that they are saying you are given segment AB, then you construct the two circles, then you ... what?

@JulianMathHelp, you haven't answered my questions in post #15. Can you see things you could construct from the diagram?
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Yes, I can see isosceles triangle, equilateral, rhombus, and an isosceles trapezoid if the given segment is AB. Is it clear that the given segment is AB because they are saying "such as AB" so it is kind of implying to use AB? What threw me off guard was that it said "when given a line segment such as AB" So I thought that the segment could be anywhere on the circle, and didn't have to be AB, which would've changed the answer.
 
Ok, so this is all of the information that I have: Both circles have the same radius, with each intersecting each other's center. Before the question, I was directed to make a rhombus using a compass and pencil (intersection of the circles connected to the centers create a rhombus). After all of this I was asked the question
 
JulianMathHelp said:
Ok, so this is all of the information that I have: Both circles have the same radius, with each intersecting each other's center. Before the question, I was directed to make a rhombus using a compass and pencil (intersection of the circles connected to the centers create a rhombus). After all of this I was asked the question
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Please just show the whole thing so we can be sure of the context.

You're now saying that there was either a long conversation, or several pages in a book, out of which the question grew. How are we supposed to tell you what was intended without seeing any of that? Clearly I was too optimistic.

It appears that the rhombus can't be part of the "what else" being asked for, since it was already covered, though you hadn't mentioned it until now. But there may be other things, too. How was the construction done? What did you start with? What was constructed as part of making the rhombus?

I will tell you that my guess as to what they might expect you to see is the perpendicular bisector of the given line AB, because that's the one thing you haven't mentioned, and it's very important. In any case, it's an open-ended question, and it's too vague to be sure what they want.
 
Ok, I know everything now, and answered the question. The last thing that I need clarification for is what indicated that the given segment is AB? (Sorry for asking this, it's probably very obvious, but I mainly speak chinese)
 
JulianMathHelp said:
Ok, I know everything now, and answered the question. The last thing that I need clarification for is what indicated that the given segment is AB? (Sorry for asking this, it's probably very obvious, but I mainly speak chinese)
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I hope you aren't telling us that the original question was in Chinese, so you are asking about the meaning of a question that you have translated, and we don't even have access to what was said at all. Are you asking about the meaning of an English sentence, or not? If not, you'll have to ask a Chinese speaker, since this is a question about the meaning of words.

But if the question was exactly the English words, "What else can this diagram help you construct when given a line segment such as AB¯?", then what indicates that the given segment is AB is the phrase, "when given a line segment such as AB"! What else could this mean? AB in the picture is an example of a line segment you would be given, on which you would construct the two circles.

But, again, meaning is determined in context, so if you want a definite answer, you must show us the entire context, as I requested. If you don't, then we don't know what is being referred to, because we don't know how AB was first introduced.
 
Ok so
1) Make two circles in which each circle intersects the center of the other circle.
2) Name the intersection of each point A and B
3) Connect the intersections of the circles and the centers of each circle, what do you get? (It’s a rhombus)
4) the question I asked initially.

is the case still the same?
No, it’s in English, and I speak Chinese
 
In 2) A more clarified explanation is: Name the center of one circle (which is intersected by the other) "A" while the other is named "B".
 
If they originally started with circles and later named the centers A and B, then my best guess is that they are asking you to reverse the process in your mind and suppose that you had first been given the segment AB, and then construct the two circles using the already-named points A and B. There is really nothing different, except that if the second center had been chosen after the first circle was drawn, in which case the new construction would start with making a circle with given center A, passing through B rather than arbitrary.

The answer could be any figure not already mentioned explicitly; the perpendicular bisector is one of them, but so is an equilateral triangle, if not previously discussed.

Ultimately, though, when you don't understand a question given by a teacher, you ask the teacher! I'm always happy to help a foreign student with English, even during exams. (And I tell American students that they, too, can ask what a question means. I'll let them know if it's a vocabulary item they are being tested on, so I can't help.)
 
Dr.Peterson said:
There is really nothing different, except that if the second center had been chosen after the first circle was drawn, in which case the new construction would start with making a circle with given center A, passing through B rather than arbitrary.
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I don’t really understand this part, what do you mean that the second center was already chosen after the first circle was drawn? I also don’t get the arbitrary part. Anyway, you clarified my doubts by telling me the given segment was AB because it said such as AB, so thank you!!! Also, it doesn’t really matter if we reverse the process right? All we need to do is connect A and B to create segment AB in the diagram, and see what we can create from there right?
 
Your brief summary of the context indicated that the original construction did not start with two named points A and B, but did not make it clear what it DID start with. (Is it really impossible for you to show us the actual source? Was it just a conversation, and not in a book? You haven't said. It would really save time and trouble if you could show it all.) So I had to guess at one of two possible constructions (which is why I had to say "if ...").

If they started with two points (unnamed) and then drew a circle with each point as center, and passing through the other, then there is absolutely no difference if the points had been named. Starting with a segment AB, you would do exactly the same construction.

But you said they started with "Make two circles in which each circle intersects the center of the other circle." This could mean that you don't have both points at the start, but just put the point of a compass somewhere (which will be called A later) and draw a circle, without worrying about what its radius is. Then you would pick any point on that circle -- this is what "arbitrary" means, that it is not given to you, but randomly chosen. That point, which will be called B, will be the center of the second circle, which you draw by using AB as the radius.

That construction would be technically different from one in which A and B are given (though not initially named). But it would not be a significant difference.
 
I still don't really see anything that would change besides the fact that the radius will be the same (always) for the first option, while the radius for the second option could be anything. However, I don't see how that affects the problem. Like I said earlier, it doesn’t really matter if we reverse the process right? All we need to do is connect A and B to create segment AB in the diagram, and see what we can create from there right?
 
Yes, that's the point. As far as your question is concerned, there is no difference.
 
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