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In the coordinate plane, points (a,b) and (c,d) are [#permalink]
09 Aug 2016, 16:11
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a > c In the coordinate plane, points (a,b) and (c,d) are equidistant from the origin.
Quantity A 
Quantity B 
B 
D 
A) The quantity in Column A is greater. B) The quantity in Column B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.




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Re: In the coordinate plane, points (a,b) and (c,d) are [#permalink]
09 Aug 2016, 17:12
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GREhelp wrote: Manhattan Prep: 5LB Book In the coordinate plane, points (a,b) and (c,d) are equidistant from the origin. a > c Quantity A B Quantity B D Here we have 2 points namely X (a,b) and Y (c,d). Now the points are equidistant from origin. \(a^2 + b^2 = c^2 + d^2\) ........ 1 Given that \(a > c\) or \(a^2 > c^2\) adding\(b^2\) on both sides \(a^2 + b^2 > c^2 + b^2\) from eqn 1 \(c^2 + d^2 > c^2 + b^2\) or \(d^2 > b^2\) or \(d > b\) Hence option B is correct.
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Re: In the coordinate plane, points (a,b) and (c,d) are [#permalink]
10 Aug 2016, 00:37
Please follow the rules for posting in verbal section. Use the tags, in particular. Regards
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Re: In the coordinate plane, points (a,b) and (c,d) are [#permalink]
10 Aug 2016, 11:08
Hi Sandy, Thanks for your response, That was a huge help. I understand how you solved the question and steps taken. However, how did you know when you first looked at the question to do a^2 + b^2 = c^2 + d^2 ????
I understand how you got a^2 > c^2 its because the a > c which means that A and C can not be negative as a result you did a^2 >c^2. I'm just trying to make sure I understand the underlying concept so I don't make the same mistake again.



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Re: In the coordinate plane, points (a,b) and (c,d) are [#permalink]
10 Aug 2016, 13:02
GREhelp wrote: Hi Sandy, Thanks for your response, That was a huge help. I understand how you solved the question and steps taken. However, how did you know when you first looked at the question to do a^2 + b^2 = c^2 + d^2 ????
I understand how you got a^2 > c^2 its because the a > c which means that A and C can not be negative as a result you did a^2 >c^2. I'm just trying to make sure I understand the underlying concept so I don't make the same mistake again. Hi Grehelp, Well actually I solved the problem mentally. I knew that a > c so b < d for the two points to be equidistant from origin. This usually comes with a bit of experience and understanding of math over time. However there is a Hack. Whenever faced with a problem like this one, try and write down all the equations from a problem statement and try to put one equation into another and check if you find some new info. This usually works. In this case we had only 2 equations. I just tried to combine them to form a new one. With some practice you can solve these problems easily as well. Regards,
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Re: In the coordinate plane, points (a,b) and (c,d) are [#permalink]
28 Feb 2018, 14:34
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It's answer should be choice B. Kindly correct the OA. Here's how: Using distance equation: Distance of point (a,b) from origin(0,0) = (a  0)^2 + (b  0)^2 = a^2 + b^2 Similarly, Distance of point (c,d) from origin(0,0) = (c  0)^2 + (d  0)^2 = c^2 + d^2 As, both distances are equal, so a^2 + b^2 = c^2 + d^2 Now, according to the given condition, absolute value of a is greater than that of d. Thus, in order for making the Left Hand Side (L.H.S) equals to Right Hand Side (R.H.S) of the equation: a^2 + b^2 = c^2 + d^2, we must come to the point that the absolute value of b must always be less that that of d. So, Quantity b is greater always. Thus choice B is correct.
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Re: In the coordinate plane, points (a,b) and (c,d) are [#permalink]
09 Mar 2018, 02:39
The answer given to this question is definitely wrong, it should be B, as explained by sandy earlier.



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Re: In the coordinate plane, points (a,b) and (c,d) are [#permalink]
09 Mar 2018, 04:04
Please change the OA to B instead of A.



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Re: In the coordinate plane, points (a,b) and (c,d) are [#permalink]
09 Mar 2018, 15:38
Done. Thank you.
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Re: In the coordinate plane, points (a,b) and (c,d) are [#permalink]
02 Feb 2019, 13:13
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GREhelp wrote: a > c In the coordinate plane, points (a,b) and (c,d) are equidistant from the origin.
Quantity A 
Quantity B 
B 
D 
Here's another approach: KEY PROPERTIES: If x² > y² then x > y If x > y then x² > y² GIVEN: (a,b) and (c,d) are equidistant from the origin. The origin has coordinates (0, 0) When we apply the formula for finding the distance between two points, we get: The distance between (a, b) and (0, 0) = √[(a  0)² + (b  0)²] = √(a² + b²) The distance between (c, d) and (0, 0) = √[(c  0)² + (d  0)²] = √(c² + d²) So, we can write: √(a² + b²) = √(c² + d²) Square both sides to get: a² + b² = c² + d² Subtract c² from both sides to get: a² + b²  c² = d² Subtract b² from both sides to get: a²  c² = d²  b²GIVEN: a > cThis also tells us that a² > c² If we subtract c² from both sides we get: a²  c² > 0Since, we know that a²  c² = d²  b², we can also conclude that d²  b² > 0Now take d²  b² > 0 and add b² to both sides to get: d² > b² Finally, if d² > b², then we know that d > b Answer: B Cheers, Brent
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Re: In the coordinate plane, points (a,b) and (c,d) are
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