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

[vanessa.kitchen]

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.

[gokul_nair1984]

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.

[tim]

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..

[Martin_G]

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..

(I came across this thread by google, I hope it is okay to bump it.)

I am not really following here. What do you mean by 'try the problem again with all the minus signs replaced by plus signs and you'll see that the answer is E' ?

If I plug in 3 for A and 4 for B and I would change the plus signs I would get:

(3+(1+3))/2 = 3.5
((1+4)+4)/2 = 4.5

According to your post, if I follow correctly, these numbers would not be the coordinates of the midpoint? Why is that?


Also, different question regarding this Prep Q:
I answered this question correctly because, like Gokul stated, I figured you'd need both statements either way?

Is it however possible to be presented with 1 sole statement being sufficient? And how would I recognize it?

Thanks in advance.

[RonPurewal]

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..

(I came across this thread by google, I hope it is okay to bump it.)

I am not really following here. What do you mean by 'try the problem again with all the minus signs replaced by plus signs and you'll see that the answer is E' ?

From what I can tell, Tim thought that the previous poster was saying, basically, "If I have both equations, I can find the exact coordinates of C and D."
This is false"”even with both statements you still don't have the exact coordinates of C and D, but you can find the exact coordinates of the midpoint between C and D (which is, of course, the only thing that matters in this problem).

Tim was telling the poster to try the problem with (a, 1 + b) and (1 + a, b) instead of the current statements, just as proof that the two statements together don't guarantee a unique set of coordinates for C or D.