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:

In the rectangular coordinate plane points X and Z lie on [#permalink]

Show Tags

18 Feb 2012, 16:28

3

This post received KUDOS

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

15% (low)

Question Stats:

85% (02:13) correct
15% (01:42) wrong based on 109 sessions

HideShow timer Statistics

Attachment:

Distance.PNG [ 4.74 KiB | Viewed 4763 times ]

In the rectangular coordinate plane points X and Z lie on the same line through the origin and points W and Y lie on the same line through the origin. If a^2+b^2=c^2+d^2 and e^2+f^2=g^2+h^2, what is the value of length XZ – length WY?

In the rectangular coordinate plane points X and Z lie on the same line through the origin and points W and Y lie on the same line through the origin. If a^2+b^2=c^2+d^2 and e^2+f^2=g^2+h^2, what is the value of length XZ – length WY?

A. -2 B. -1 C. 0 D. 1 E. 2

Since X and Z lie on the same line through the origin then the distance between X and Z will be equal to the sum of the individual distances of X and Z from the origin: \(\sqrt{c^2 + d^2}+\sqrt{g^2 + h^2}\);

The same way, the distance between W and Y will be equal to the sum of the individual distances of W and Y from the origin: \(\sqrt{a^2 + b^2}+\sqrt{e^2 + f^2}\);

Re: In the rectangular coordinate plane points X and Z lie on [#permalink]

Show Tags

24 Feb 2012, 00:24

A quick question: All we know is that the line passes through X, origin, and Z vs. the second line passes through W, origin, and Y. There is no indication that the points are equidistant with respect to the origin. Can we assume this or is there a part of the wording from the original question missing?

The way I approached it: sqrt ((g-c)^2+(h-d)^2) = sqrt ((a-e)^2+ (b-f)^2) This simplifies to gc+hd = ae +bf.

A quick question: Nowhere in the question does it say that the two points are equidistant right? How can we say that the distance from origins are same? Please explain.

The formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\). Now, if one point is origin, coordinate (0, 0), then the formula can be simplified to: \(D=\sqrt{x^2+y^2}\).

Hence for our original question: a^2+b^2=c^2+d^2 means that points X and W are equidistant from the origin and e^2+f^2=g^2+h^2 means that points Y and Z are equidistant from the origin.

Next, since X and Z lie on the same line through the origin and W and Y lie on the same line through the origin then the distance of line segments XZ and WY is equal (for algebraic proof see above post).

Re: In the rectangular coordinate plane points X and Z lie on [#permalink]

Show Tags

30 May 2013, 20:29

enigma123 wrote:

Attachment:

Distance.PNG

In the rectangular coordinate plane points X and Z lie on the same line through the origin and points W and Y lie on the same line through the origin. If a^2+b^2=c^2+d^2 and e^2+f^2=g^2+h^2, what is the value of length XZ – length WY?

The above will give the answer of zero if we substitute the values from question stem.

Another way to solve this is if I draw a line segment from origin to point W (say w) and origin to point X (say x) will be hypotenuse defined by \(\sqrt{a^2 +b^2}\)= \(\sqrt{w^2}\) and \(\sqrt{c^2 +d^2}\)= \(\sqrt{x^2}\)

So you will end up with w=x and y=z --> (x+z) -(y+z) =0

Re: In the rectangular coordinate plane points X and Z lie on [#permalink]

Show Tags

29 Oct 2014, 08:28

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: In the rectangular coordinate plane points X and Z lie on [#permalink]

Show Tags

15 Nov 2015, 14:27

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.
_________________

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...