what is wrong in my ans?

Question

in the question to Lance
http://answers.yahoo.com/question/index;_ylt=AgsmlA0tvjGud0EPP_iiziHsy6IX?qid=20061007032618AAcX3mr
my explanation is
you are right in general case. But please consider this particular case if O is origin
OA =1 as sqrt(sin^ 2t + cos ^2 t) = 1
OB = 1
so distance from origin to A and B are same.

So perpendicular must bisect the line AB.
So my solution is correct.
If you still feel that I have done a mistake then I may be informed how.

I am asking this because lance mentioned I cannot use mid point formula

he did not mention not to use this formla. After I used the formula he mentioned this beow

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A question of Coordinate Geometry: Help Maths Geniuses out There!?

Find the perpendicular distance from origin of a line joining the points A (cosθ, sinθ) and B (cosφ, sinφ).
Additional Details

1 week ago
math_kp, your answer is incorrect.
The perpendicular from origin does not necessarily bisect the line segment AB, so you cannot use mid point formula..

Which is incorrect because in this particular case perpenidualr bisects.

Secondly are we not supposed to use special case and failing which we go the general.

Answer 1

The only thing I can think of is when A and B are opposite each other--180 degrees. In that case, your method doesn't work, because there isn't a method for perpendicular distance...or it's 0.

Answer 2

I think your solution will give the correct answer because, in this special case, the two points must lie on the circumference of a circle centred at the origin (because both coordinates are defined as (sin a, cos a) where a may represent any two angles and, without any further information, one must assume the angles to be measured conventionally at the origin), so a line through both points must be a chord. Using the midpoint theorem to find the point of intersection will therefore give the correct result for the point of intersection.

However, a correct answer does not always mean a correct solution. I would rather say that your answer may be correct but using the distance method would probably be a more robust solution.

Answer 3

His point is valid, I think, in that you found a specific answer where one of generality is asked for.

I didn't look over the mechanics of your work, so much as that I looked over what he was saying. I also see your point too, in that it does indeed pertain to his question, however his question was still asking for a result that woudl give ANY perp, and you gave one that provided a specific one.

I've been snagged on this kind of 'technicality' also. But usually generalities are what is required, unless the machanics of a certain procedure as being tested.

I do think he should have pointed out the generality rater than have it be assumed, as most math questions do. It's part of the vernacular of math, and it's part of the creativity too actually. So, while I think you did good work and provided an answer, I think it comes down to the fact that he simply needed an answer that is more general than what you provided.

And check me of I'm wrong, but since when did coordinate geometry utilize trig? I thought it was all, points, lines and planes without trig. Hmmmmmmmmm....should I post that as a quiestion myself perhaps, or do you know?

Answer 4

The problem is whether the midpoint formula is valid for the extreme cases: the angles are equal or they are opposite.

As a (former) mathematician, my sympathies are with you. As an indication I think your method is fine. To be absolutely correct you would have to examine the proof of the midpoint formula to see if there are any restrictions that would affect this. If at some point they restrict the angle - divide by it, or assume a < 180 - then the proof would be invalid for those cases. I don't see in this case that there would be any such restrictions, but to make your case you would need to check.

Answer 5

do no longer problem approximately it some human beings p.c.. the 'superb answer' because of the fact the only they believe the least in basic terms so as that they they are in a position to tell the guy off and make useful they study it with out having the flexibility to respond. that's all in basic terms for exciting right here, do no longer take it too heavily. Edit i think of she became the chooser, yet she seems disturbed by her incorrect decision :-)

Answer 6

Hey! Who am I to argue with Lance?

Answer 7

the question of lance is stupid
he doesnt tell what the angles are.
stay away rfom him.