Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

50% (02:16) correct
49% (01:08) wrong based on 65 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 1404 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