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If a and b are positive numbers, what are the coordinates of

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vanessa.kitchen
 Post subject: If a and b are positive numbers, what are the coordinates of
 Post Posted: Sun Oct 03, 2010 11:35 pm 
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Course Students


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If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?

1) The coordinates of C are (a, 1-b)

2) The coordinates of D are (1-a, b)

Data Sufficiency: A, B, C, D, E

Answer is C.

How do you begin to approach this problem? Plug in numbers? Algebra? I understand the solution of adding the x coordinate together and dividing by two (to get the midpoint coordinate) and adding the y coordinates together and dividing by two, leaving you with the coordinate: (1/2, 1/2). However, I don't think I would see this automatically on the test...is there an easier way?

Thanks.
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gokul_nair1984
 Post subject: Re: If a and b are positive numbers, what are the coordinates of
 Post Posted: Mon Oct 04, 2010 3:32 am 
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Students


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vanessa.kitchen wrote:
If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?

1) The coordinates of C are (a, 1-b)

2) The coordinates of D are (1-a, b)


You could either do it by picking numbers or arrive at the answer using algebra.You could also by heart the rule of a midpoint. ie; The coordinates of the midpoints will be the average of the coordinates of the extremes.

The midpoint of X(a,b) and Y(c,d) is given by (a+c)/2 and (b+d)/2.

Or you could logically think about the question. In order to find the midpoint you will need to know the extreme points' coordinates and that is provided only by combining both the statements.
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tim
 Post subject: Re: If a and b are positive numbers, what are the coordinates of
 Post Posted: Fri Oct 08, 2010 1:47 am 
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ManhattanGMAT Staff


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Location: Southwest Airlines, seat 21C
thanks, Gokul. keep in mind that even though we know we can find the midpoint, we do need to verify that the midpoint will be a specific set of coordinates, i.e. involving no variables. if any variables show up in the end, your information is insufficient. try the problem again with all the minus signs replaced by plus signs and you'll see that the answer is E..

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Tim Sanders
Manhattan GMAT Instructor
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