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by ramyaravindran » Thu Feb 18, 2010 1:33 pm
I am not sure about the source of the question. I also do not have the OA. Can someone help with this question?

If a point in a particular co-ordinate system is (2,9) and in another co-ordinate system is (-8,81) then by how many degrees should the first co-ordinate axis be rotated to get the second co-ordinate axis?
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by ajith » Thu Feb 18, 2010 1:45 pm
ramyaravindran wrote:I am not sure about the source of the question. I also do not have the OA. Can someone help with this question?

If a point in a particular co-ordinate system is (2,9) and in another co-ordinate system is (-8,81) then by how many degrees should the first co-ordinate axis be rotated to get the second co-ordinate axis?
x' = x cos A + y sin A
y' = -x sin A + y cos A

-8 = 2 Cos A+ 9 Sin A
81 = -2 Sin A + 9 cos A

These equations are inconsistent with the given values, if you have the good values, we could have given a shot at finding A
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by harsh.champ » Thu Feb 18, 2010 2:00 pm
ajith wrote:
ramyaravindran wrote:I am not sure about the source of the question. I also do not have the OA. Can someone help with this question?

If a point in a particular co-ordinate system is (2,9) and in another co-ordinate system is (-8,81) then by how many degrees should the first co-ordinate axis be rotated to get the second co-ordinate axis?
x' = x cos A + y sin A
y' = -x sin A + y cos A

-8 = 2 Cos A+ 9 Sin A
81 = -2 Sin A + 9 cos A

These equations are inconsistent with the given values, if you have the good values, we could have given a shot at finding A
I guess this is a very high level co-ordinate geometry question involving the shifting of the co-ordinate axis.
Can such problems be asked on the GMAT??
I guess it should be categorized as a "Challenge Problem".

Anyways for knowledge purposes,Ajith -Can you explain what do you mean by the statement that the equations are inconsistent with the given values.
These equations are inconsistent with the given values, if you have the good values, we could have given a shot at finding A
How do we check for consistency in an equation??Is it similar to unique solns.,infinite solns. and no soln??
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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by ajith » Thu Feb 18, 2010 2:05 pm
harsh.champ wrote: Anyways for knowledge purposes,Ajith -Can you explain what do you mean by the statement that the equations are inconsistent with the given values.
These equations are inconsistent with the given values, if you have the good values, we could have given a shot at finding A
How do we check for consistency in an equation??Is it similar to unique solns.,infinite solns. and no soln??
Yes It is similar to unique solns.,infinite solns. and no soln
so as to why these equations are inconsistent, square and add them and see it for yourself.
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by harsh.champ » Thu Feb 18, 2010 2:36 pm
ajith wrote:
harsh.champ wrote: Anyways for knowledge purposes,Ajith -Can you explain what do you mean by the statement that the equations are inconsistent with the given values.
These equations are inconsistent with the given values, if you have the good values, we could have given a shot at finding A
How do we check for consistency in an equation??Is it similar to unique solns.,infinite solns. and no soln??
Yes It is similar to unique solns.,infinite solns. and no soln
so as to why these equations are inconsistent, square and add them and see it for yourself.
Well taking the square of the 1st equation :- -8 = 2 Cos A+ 9 Sin A
we get 64 = 4 (CosA)^2 + 81(SinA)^2 +36SinA.CosA-(1)
2nd equation we have:-
81 = -2 Sin A + 9 cos A
Thus, 6561 = 4 (SinA)^2 + 81(CosA)^2 -36SinA.CosA -(2)

Adding 1 and 2 , we get that 6642 = 4 + 81 ....Hence the values are inconsistent.




Hey ajith,
I learnt the following technique for determining the consistency:-
Let the coefficients of the equations be a1,b1,c1 and a2,b2,c2 respectively.
Then if a1/a2 (is not equal to) b1/b2 (which is not equal to) c1/c2 we get inconsistent solns.
I guess this is a shorter approach to check the consistency.
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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by ajith » Thu Feb 18, 2010 2:42 pm
harsh.champ wrote: Hey ajith,
I learnt the following technique for determining the consistency:-
Let the coefficients of the equations be a1,b1,c1 and a2,b2,c2 respectively.
Then if a1/a2 (is not equal to) b1/b2 (which is not equal to) c1/c2 we get inconsistent solns.
I guess this is a shorter approach to check the consistency.
x+y =3
x-y =1

are totally consistent despite a1/a2 (is not equal to) b1/b2 (which is not equal to) c1/c2

a1/a2 =1 b1/b2 = -1 c1/c2 =3

If two of these are equal and if the third is not equal then the equations are not consistent
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by shashank.ism » Sun Feb 21, 2010 8:46 pm
ramyaravindran wrote:I am not sure about the source of the question. I also do not have the OA. Can someone help with this question?

If a point in a particular co-ordinate system is (2,9) and in another co-ordinate system is (-8,81) then by how many degrees should the first co-ordinate axis be rotated to get the second co-ordinate axis?
you just draw a straight line from centre to the given points and find the slope between the two
use trigonometric formula to find the angle between the two and ur done ...u have actually found out the angle between the two axes.
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