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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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]

Show Tags

29 Sep 2013, 19:43

3

This post received KUDOS

18

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

61% (01:57) correct
39% (01:00) wrong based on 427 sessions

HideShow timer Statistics

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?

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 10932 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]

Show Tags

21 Oct 2013, 23:03

2

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]

Show Tags

02 Nov 2013, 10:59

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]

Show Tags

02 Nov 2013, 22:43

1

This post received KUDOS

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]

Show Tags

03 Nov 2013, 01:31

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]

Show Tags

15 Jan 2015, 10:28

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

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

Show Tags

20 Jun 2015, 06:14

Why cant a line that pass through (2,2) and make 45 degrees(slope 1) with X axis and that also splits the rectangle into two quadrilaterals be assumed ?

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

Why cant a line that pass through (2,2) and make 45 degrees(slope 1) with X axis and that also splits the rectangle into two quadrilaterals be assumed ?

CONCEPT : The readers need to know that a rectangle can be divided into two equal area by a Straight line only when the straight line passes through the Centre of the Rectangle (Intersection of its two diagonals) Draw a figure and know it for yourself.

The point of Intersections of the diagonals will be the midpoint of any diagonal i.e. Midpoint of (0,0), and (7,4) OR Midpoint of (0,4) and (7,0)

i.e. Either [(0+7)/2, (0+4)/2] OR [(0+7)/2, (4+0)/2] = [3.5, 2]

Slope of line passing through points (2,2) and (3.5,2) = (2-2)/(3.5-2) = 0

P.S. Line passing through (2,2) and slope =1 will also pass through origin and will divide the rectangle into One triangle and another Trapezium which will not have equal Areaa _________________

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

Show Tags

16 Aug 2016, 08:49

I am unable to understand why cant it be a diagonal and why horizontal line. The rectangle has 1 pair of sides equal , the diagonal from origin passing thru 2,2 will divide into 2 parts that is equal. Please tell me why we are considering horizontal line and not the diagonal.

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

Show Tags

08 Sep 2016, 17:02

megha_2709 wrote:

I am unable to understand why cant it be a diagonal and why horizontal line. The rectangle has 1 pair of sides equal , the diagonal from origin passing thru 2,2 will divide into 2 parts that is equal. Please tell me why we are considering horizontal line and not the diagonal.

Regards Megha

A diagonal is not the only line that divides the area into two equal halves. Nor is the horizontal line. A vertical line could also divide a rectangle into two equal facts. In fact, if there is only one point given within a rectangle, we can draw a line that would not be horizontal, vertical or diagonal, that would divide a rectangle into two trapeziums of equal area. However, we need to identify which of the following points are on a line that divides the rectangle into two equal halves. A figure approach, as demonstrated by bunuel, helps.

However, if you wish to check through an extended version, find the equation of the line that would make the diagonal of the rectangle. You'd find that the point (2,2). does not lie on the diagonal. Also, it would not lie on a line that is vertical and that divides the rectangle into two equal halves. Another way of looking at the question is that the breadth of the rectangle is 4 and the length is 7. So a horizontal line with y co-ordinate 2 will for sure divide the rectangle into two equal halves. Also, a vertical line with x co-ordinate 3.5 would do the same job.

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

Show Tags

09 Sep 2016, 22:10

I was initially confused that for splitting the triangle into 2 equal areas, diagonal might be required. But then, when the graph is plotted, the line that goes through (2,2) will go straight and have coordinates (0,2) & (7,2). The area formed is half of the rectangle and the slope would be 0. [Distance between two points (2,2) - (0,2)].

gmatclubot

Re: The vertices of a rectangle in the standard (x,y) coordinate
[#permalink]
09 Sep 2016, 22:10

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...