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The vertices of a rectangle in the standard (x,y) coordinate

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The vertices of a rectangle in the standard (x,y) coordinate [#permalink] New post 29 Sep 2013, 18:43
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The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (7,0) and (7,4). If a line through (2,2) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?

A. 0
B. 2/5
C. 4/7
D. 1
E. 7/4

I got confused on this question. Can you show a good method of doing it?
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Sep 2013, 22:50, edited 1 time in total.
Edited the question.
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Re: The vertices of a rectangle in the standard (x,y) coordinate [#permalink] New post 29 Sep 2013, 22:52
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teeva wrote:
The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (7,0) and (7,4). If a line through (2,2) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?

A. 0
B. 2/5
C. 4/7
D. 1
E. 7/4

I got confused on this question. Can you show a good method of doing it?


Look at the diagram below:
Attachment:
Rectangle.png
Rectangle.png [ 7.17 KiB | Viewed 2272 times ]
In order the line to divide the rectangle into two equal parts it must be horizontal. The slope of any horizontal line is zero.

Answer: A.

For more on Coordinate Geometry check here: math-coordinate-geometry-87652.html

Hope it helps.
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Re: The vertices of a rectangle in the standard (x,y) coordinate [#permalink] New post 21 Oct 2013, 22:03
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First I assumed the line passes through the origin and is a diagonal of the rectangle making the slope 1. But then I realized that the slope can't be '1' because only a square would have a slope of 1. Since this is a rectangle, its slope has to be something else.

This is a good problem where the grid lines on the worksheet come in handy. Just need to make sure to draw the sketch to scale.
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Re: The vertices of a rectangle in the standard (x,y) coordinate [#permalink] New post 02 Nov 2013, 09:59
Bunuel wrote:
teeva wrote:
The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (7,0) and (7,4). If a line through (2,2) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?

A. 0
B. 2/5
C. 4/7
D. 1
E. 7/4

I got confused on this question. Can you show a good method of doing it?


Look at the diagram below:
Attachment:
Rectangle.png
In order the line to divide the rectangle into two equal parts it must be horizontal. The slope of any horizontal line is zero.

Answer: A.

For more on Coordinate Geometry check here: math-coordinate-geometry-87652.html

Hope it helps.


Why did you not check to see if it is the diagonal of the rectangle?
Is it not possible for the diagonal to split it into 2 equal shapes?
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Re: The vertices of a rectangle in the standard (x,y) coordinate [#permalink] New post 02 Nov 2013, 21:43
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ronr34 wrote:
Why did you not check to see if it is the diagonal of the rectangle?
Is it not possible for the diagonal to split it into 2 equal shapes?



It is not possible to have the point (2,2) on the diagonal. Had it been on the diagonals, the slope of this line would be : \frac{4-0}{7-0} = \frac{2-0}{2-0} which is obviously not the case as these 2 values are different.
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Re: The vertices of a rectangle in the standard (x,y) coordinate [#permalink] New post 03 Nov 2013, 00:31
mau5 wrote:
ronr34 wrote:
Why did you not check to see if it is the diagonal of the rectangle?
Is it not possible for the diagonal to split it into 2 equal shapes?



It is not possible to have the point (2,2) on the diagonal. Had it been on the diagonals, the slope of this line would be : \frac{4-0}{7-0} = \frac{2-0}{2-0} which is obviously not the case as these 2 values are different.


Yes this is what I thought.
I just didn't understand if it was a given that we need to check it, or if there was
another way of knowing without making this equation and checking.
Re: The vertices of a rectangle in the standard (x,y) coordinate   [#permalink] 03 Nov 2013, 00:31
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