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14 Jan 2015, 02:28
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
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Question Stats:
78% (01:06) correct
22%
(01:24)
wrong
based on 281
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If r and s are positive numbers, what are the coordinates of the midpoint of line segment MN in the xy-plane?
(1) The coordinates of M are (r; 3 - s).
(2) The coordinates of N are (3 - r; s).
Kudos for a correct solution.
(1) The coordinates of M are (r; 3 - s).
(2) The coordinates of N are (3 - r; s).
Kudos for a correct solution.
14 Jan 2015, 11:51
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Without going rephrasing the question, we can directly look at the statements. The only thing we see is that we need some kind of information about the two points M and N.
Looking at the statements we see that neither statements contains information about both points, so if we can get enough information to answer the question, it can only be from both statements combined. With that we can conclude:
To analyse the statements, lets make a the convention that the coordinates of M are larger. If that should not be the case, the result should differ by a minus.
The coordinates of the mid point of the line are the smaller coordinate plus half the difference between the larger and the smaller. Therefore, the x-coordinate is:
\(x=r-\frac{r-(3-r)}{2}\frac{2r-(r-(3-r))}{2}=\frac{2r-2r+3}{s}=\frac{3}{2}\)
and the y-coordinate is:
\(3-s-\frac{(3-s)-s}{2}=\frac{6+2s-3-2s}{2}=\frac{3}{2}\)
As both coordinates are independent of r and s, we know that answer C is correct.
Looking at the statements we see that neither statements contains information about both points, so if we can get enough information to answer the question, it can only be from both statements combined. With that we can conclude:
To analyse the statements, lets make a the convention that the coordinates of M are larger. If that should not be the case, the result should differ by a minus.
The coordinates of the mid point of the line are the smaller coordinate plus half the difference between the larger and the smaller. Therefore, the x-coordinate is:
\(x=r-\frac{r-(3-r)}{2}\frac{2r-(r-(3-r))}{2}=\frac{2r-2r+3}{s}=\frac{3}{2}\)
and the y-coordinate is:
\(3-s-\frac{(3-s)-s}{2}=\frac{6+2s-3-2s}{2}=\frac{3}{2}\)
As both coordinates are independent of r and s, we know that answer C is correct.
15 Jan 2015, 05:02
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on higher level, to locate any line segment, we need two points.
and to find the mid points of a line segment, we need to locate the line segment first.
so clearly both the statements alone are not sufficient to answer the question.
Combining we get----
(3/2,3/2)
hence option C should be the correct answer.
and to find the mid points of a line segment, we need to locate the line segment first.
so clearly both the statements alone are not sufficient to answer the question.
Combining we get----
(3/2,3/2)
hence option C should be the correct answer.
