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The vertices of a rectangle in the standard (x,y) coordinate [#permalink]
29 Sep 2013, 18:43

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Difficulty:

35% (medium)

Question Stats:

49% (02:08) correct
51% (01:05) wrong based on 87 sessions

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?

Re: The vertices of a rectangle in the standard (x,y) coordinate [#permalink]
29 Sep 2013, 22:52

Expert's post

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 [ 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.

Re: The vertices of a rectangle in the standard (x,y) coordinate [#permalink]
21 Oct 2013, 22:03

1

This post received KUDOS

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.

Re: The vertices of a rectangle in the standard (x,y) coordinate [#permalink]
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.

Re: The vertices of a rectangle in the standard (x,y) coordinate [#permalink]
02 Nov 2013, 21:43

Expert's post

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. _________________

Re: The vertices of a rectangle in the standard (x,y) coordinate [#permalink]
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.

gmatclubot

Re: The vertices of a rectangle in the standard (x,y) coordinate
[#permalink]
03 Nov 2013, 00:31