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Re: Which of the following points could lie in the same quadrant of the xy [#permalink]
kumarneupane4344 wrote:
saumik wrote:
Choose the point (a, b) = (1, -1)

A. (-b , -a) = (1, -1)
B. (–a, –b) = (-1, 1)
C. (b, –a) = (-1, -1)
D. (a, –b) = (1, 1)
E. (–b, a) = (1, 1)


Only choice A is equivalent to our assumed point, i.e, both their x and y coordinates have the same signs.
The answer is A.



Sir, will option A true for all co ordinates?


Yes, as long as you take co-ordinates from 2nd and 4th quadrants.

We assumed the point(1, -1), which is in the 4th quadrant. We proved this as true.
Let's choose (a, b) = (4, -5), which is at 2nd quadrant. Now, (-b , -a) = (5, -4). That's in the 2nd quadrant too. So this is true.

Note that points from 1st and 3rd quadrants won't hold true. We only need to prove one case as true to choose option A.
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Re: Which of the following points could lie in the same quadrant of the xy [#permalink]
saumik wrote:
kumarneupane4344 wrote:
saumik wrote:
Choose the point (a, b) = (1, -1)

A. (-b , -a) = (1, -1)
B. (–a, –b) = (-1, 1)
C. (b, –a) = (-1, -1)
D. (a, –b) = (1, 1)
E. (–b, a) = (1, 1)


Only choice A is equivalent to our assumed point, i.e, both their x and y coordinates have the same signs.
The answer is A.



Sir, will option A true for all co ordinates?


Yes, as long as you take co-ordinates from 2nd and 4th quadrants.

We assumed the point(1, -1), which is in the 4th quadrant. We proved this as true.
Let's choose (a, b) = (4, -5), which is at 2nd quadrant. Now, (-b , -a) = (5, -4). That's in the 2nd quadrant too. So this is true.

Note that points from 1st and 3rd quadrants won't hold true. We only need to prove one case as true to choose option A.



Its not mention in the question for picking up quadrant, thats where I got confused sir..
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Re: Which of the following points could lie in the same quadrant of the xy [#permalink]
2
Quote:
Its not mention in the question for picking up quadrant, thats where I got confused sir..

When we choose/assume numbers, it's important we consider all cases.
For co-ordinate geometry, while choosing points, it's better to examine 2 cases with points from 1st/3rd quadrants AND 2nd/4th quadrants.
In this problem, I assumed a co-ordinate from 2nd/4th quadrant first, just out of intuition that to get another point in the same quadrant, we may need a combo of both + and - in our assumed point. And that actually was the case, so didn't have to check the 1st/3rd quadrant case further.
Hope this helps!
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Re: Which of the following points could lie in the same quadrant of the xy [#permalink]
saumik wrote:
Quote:
Its not mention in the question for picking up quadrant, thats where I got confused sir..

When we choose/assume numbers, it's important we consider all cases.
For co-ordinate geometry, while choosing points, it's better to examine 2 cases with points from 1st/3rd quadrants AND 2nd/4th quadrants.
In this problem, I assumed a co-ordinate from 2nd/4th quadrant first, just out of intuition that to get another point in the same quadrant, we may need a combo of both + and - in our assumed point. And that actually was the case, so didn't have to check the 1st/3rd quadrant case further.
Hope this helps!


I got it. Thank you sir!
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Re: Which of the following points could lie in the same quadrant of the xy [#permalink]
1
Answer: A
1. We can't take points from the 1st quadrant and 4th quadrant as it is not possible for these options to lie in that quadrant after flipping of sign occurring in all of the options.
2. Example point: (-4, 3)
3. The point obtained from options should have (-ve, +ve)
4. We can immediately eliminate all options except A without even checking as the operation should be such that both x and y signs are flipped.
5. And Option B is even immediately eliminated as the position of x and y are not changed.
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Re: Which of the following points could lie in the same quadrant of the xy [#permalink]
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