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co-ordinate geometry

by tahitiboy » Thu Apr 08, 2010 10:04 pm
If a and b are positive numbers, what are the co-ordinates of the midpoint of line segment Cd in the xy-pane?
1. The co-ordinates of C are (a, 1-b)
2. The co-ordinates of D are (1-a, b)

Thanks.
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Source: — Data Sufficiency |
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by thephoenix » Thu Apr 08, 2010 10:37 pm
imo c
if a point divides a line in m:n ratio internally, then its coordinates are given by
x coordinates=(m*x1+n*x2)/(m+n)
y coordinates=(m*y1+n*y2)/(m+n)
here m and n are 1
and we need x1,x2 and y1 and y2

that is C
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by lunarpower » Fri Apr 09, 2010 12:45 am
thephoenix wrote:imo c
if a point divides a line in m:n ratio internally, then its coordinates are given by
x coordinates=(m*x1+n*x2)/(m+n)
y coordinates=(m*y1+n*y2)/(m+n)
here m and n are 1
and we need x1,x2 and y1 and y2

that is C
well, you have the right answer, but not really for the right reasons (at least not based on what you wrote -- maybe you actually fully understand the problem, and just aren't communicating the sum of that knowledge).

i.e., from your post, it seems that you believe that the answer to this problem is (c) merely because the statements give an expression for each coordinate.
in other words, your post doesn't convey the fact that the actual expressions (a, 1 - a, b, and 1 - b) matter!

--

remember that "a" and "b" are UNKNOWNS -- even if you have both of the statements -- so, in order for the answer to be (c), those unknowns must cancel out completely.

that is what happens here:
the x-coordinate of the midpoint is (a + (1 - a))/2, or 1/2;
and
the y-coordinate of the midpoint is ((1 - b) + b)/2, or 1/2.

therefore, the midpoint is always at (1/2, 1/2), regardless of the values of a and b. that is why the two statements together are sufficient.

--

for instance, if the problem had asked for the point that is two-thirds (or ANY fraction other than one-half) of the way from C to D, the answer to this problem would've been (e).

make sure you understand why.
Ron has been teaching various standardized tests for 20 years.

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by thephoenix » Fri Apr 09, 2010 3:21 am
awesome ron,

u are simply great.
It makes sense i completely ignored the trap of unknown quantity....
one more entry to my flash cards ......
thanks
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