Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 22 May 2015, 18:59

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the rectangular coordinate system, are the points (a, b)

Author Message
TAGS:
Senior Manager
Joined: 19 Nov 2009
Posts: 328
Followers: 5

Kudos [?]: 70 [2] , given: 44

In the rectangular coordinate system, are the points (a, b) [#permalink]  10 Apr 2010, 22:25
2
KUDOS
21
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

39% (02:08) correct 61% (01:13) wrong based on 300 sessions
In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) $$\frac{a}{b}=\frac{c}{d}$$

(2) $$\sqrt{a^2}+ \sqrt{b^2} = \sqrt{c^2} + \sqrt{d^2}$$
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Apr 2012, 07:24, edited 1 time in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 27465
Followers: 4305

Kudos [?]: 42112 [5] , given: 5957

Re: ManhttanGMAT Practice CAT [#permalink]  11 Apr 2010, 00:11
5
KUDOS
Expert's post
4
This post was
BOOKMARKED
nsp007 wrote:
In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) $$\sqrt{a^2}+ \sqrt{b^2} = \sqrt{c^2} + \sqrt{d^2}$$

Will post OA later.

In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

Distance between the point A (x,y) and the origin can be found by the formula: $$D=\sqrt{x^2+y^2}$$.

So we are asked whether $$\sqrt{a^2+b^2}=\sqrt{c^2+d^2}$$? Or whether $$a^2+b^2=c^2+d^2$$?

(1) $$\frac{a}{b}=\frac{c}{d}$$ --> $$a=cx$$ and $$b=dx$$, for some non-zero $$x$$. Not sufficient.

(2) $$\sqrt{a^2}+\sqrt{b^2}=\sqrt{c^2} +\sqrt{d^2}$$ --> $$|a|+|b|=|c|+|d|$$. Not sufficient.

(1)+(2) From (1) $$a=cx$$ and $$b=dx$$, substitute this in (2): $$|cx|+|dx|=|c|+|d|$$ --> $$|x|(|c|+|d|)=|c|+|d|$$ --> $$|x|=1$$ (another solution $$|c|+|d|=0$$ is not possible as $$d$$ in (1) given in denominator and can not be zero, so $$d\neq{0}$$ --> $$|c|+|d|>0$$) --> now, as $$|x|=1$$ and $$a=cx$$ and $$b=dx$$, then $$|a|=|c|$$ and $$|b|=|d|$$ --> square this equations: $$a^2=c^2$$ and $$b^2=d^2$$ --> add them: $$a^2+b^2=c^2+d^2$$. Sufficient.

_________________
Director
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 691
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Followers: 14

Kudos [?]: 90 [0], given: 15

Re: ManhttanGMAT Practice CAT [#permalink]  08 Sep 2010, 01:22
Bunuel, had condition (2) simply said a+b=c+d (instead of the squares and square root) how would have the answer changed?

Also in the current question - is a^2+b^2=c^2+d^2?
When I square both sides of (2), I get a^2+b^2+2sqrt(a^2b^2)=c^2+d^2+2sqrt(c^2d^2)
so if ab=cd then this is satisfied. however (1) only gives me ad=bc, how do I infer ab=cd from that? I am following a different process, but I should end up with the same answer. Not sure where am I wrong?
_________________

Consider kudos, they are good for health

Manager
Joined: 16 Mar 2010
Posts: 190
Followers: 2

Kudos [?]: 65 [0], given: 9

Re: ManhttanGMAT Practice CAT [#permalink]  09 Sep 2010, 00:42
I have a question here bunuel. How did you get a = c * x and b= d*x??

Because from this it means that x = b/d = a/c

Math Expert
Joined: 02 Sep 2009
Posts: 27465
Followers: 4305

Kudos [?]: 42112 [1] , given: 5957

Re: ManhttanGMAT Practice CAT [#permalink]  09 Sep 2010, 00:55
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
amitjash wrote:
I have a question here bunuel. How did you get a = c * x and b= d*x??

Because from this it means that x = b/d = a/c

It's the same: $$\frac{b}{d} = \frac{a}{c}$$ --> $$bc=ad$$--> $$\frac{c}{d}=\frac{a}{b}$$.

Given: $$\frac{a}{b}=\frac{c}{d}=\frac{cx}{dx}$$ (as the ratios are equal then there exist some $$x$$ for which $$a=cx$$ and $$b=dx$$).
_________________
Manager
Joined: 19 Aug 2010
Posts: 77
Followers: 3

Kudos [?]: 16 [0], given: 2

Re: points equidistant from origin? [#permalink]  16 Oct 2010, 14:52
(1) knowing these proportions does not help me solve it, because for example if 3/1 = 9/3 , point (a,b) will be closer to the origin than point (b,c)

(2) this statement tells that |a|+|b|=|c|+|d| , which is still not sufficient because we lack information about the correlation between |a| and |b|,and |c|and|d|.

But if we combine the two statements together we will have this correlation from statement (1) and then both statements taken together will be sufficient.

Retired Moderator
Joined: 02 Sep 2010
Posts: 806
Location: London
Followers: 82

Kudos [?]: 582 [3] , given: 25

Re: points equidistant from origin? [#permalink]  16 Oct 2010, 15:21
3
KUDOS
1
This post was
BOOKMARKED
Orange08 wrote:
In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

a. $$a/b = c/d$$

b. $$\sqrt{a^2}+\sqrt{b^2} = \sqrt{c^2} + \sqrt{d^2}$$

Distance of $$(x,y)$$ from origin is $$\sqrt{x^2+y^2}$$
So we need to answer $$\sqrt{a^2+b^2}=\sqrt{c^2+d^2}$$ ?

(1) a/b=c/d ... doesnt really help in proving or disproving. Insufficient

(2) This is equivalent to saying $$|a|+|b|=|c|+|d|$$. Again insufficient to say anything about the statement we have.

(1+2) a/c=b/d=x say (needs, c,d to be non zero)

a = cx
b = dx

|a|+|b|=|c|+|d|
|cx| - |c| = |d| - |dx|
|c|(|x|-1)=|d|(1-|x|)
(|c|+|d|)(|x|-1)=0
Since c,d are non-zero means |x|=1
So either a=c & b=d OR a=-c or b=-d
Either case a^2=c^2 and b^2=d^2
Hence $$\sqrt{a^2+b^2}=\sqrt{c^2+d^2}$$
Sufficient

_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5536
Location: Pune, India
Followers: 1366

Kudos [?]: 6950 [5] , given: 178

Re: Difficult Geometry DS Problem [#permalink]  12 Jan 2011, 18:43
5
KUDOS
Expert's post
2
This post was
BOOKMARKED
abmyers wrote:
In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) $$\sqrt{a^2}+\sqrt{b^2} = \sqrt{c^2} + \sqrt{d^2}$$

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

You can take values to solve this question quickly:

Statement 1: a/b = c/d
(a,b) and (c,d) may be equidistant from the origin e.g. (1, 1) and (-1, -1) or they may not be e.g. (1, 1) and (2, 2). Not sufficient.

Statement 2: $$\sqrt{a^2}+\sqrt{b^2} = \sqrt{c^2} + \sqrt{d^2}$$
That is, |a|+|b|=|c|+|d|
(a,b) and (c,d) may be equidistant from the origin e.g. (1, 3) and (-1, -3) or they may not be e.g. (1, 3) and (2, 2)

Using both together, |a|+|b|=|c|+|d| and a/b = c/d.
This means that if a/c = 1/2, c/d cannot be 2/4 or -3/-6 etc. c/d has to be either 1/2 or (-1)/(-2). Similarly, if a/b = (-1)/2, c/d = (-1)/2 or 1/(-2))
Any pair of such points will be equidistant. Answer (C).
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 27 Nov 2011 Posts: 7 Location: India Concentration: Technology, Marketing GMAT 1: 660 Q47 V34 GMAT 2: 710 Q47 V41 WE: Consulting (Consulting) Followers: 0 Kudos [?]: 17 [0], given: 4 Re: ManhttanGMAT Practice CAT [#permalink] 27 May 2012, 22:56 Bunuel wrote: nsp007 wrote: In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin? (1) a/b = c/d (2) $$\sqrt{a^2}+ \sqrt{b^2} = \sqrt{c^2} + \sqrt{d^2}$$ Will post OA later. In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin? Distance between the point A (x,y) and the origin can be found by the formula: $$D=\sqrt{x^2+y^2}$$. So we are asked whether $$\sqrt{a^2+b^2}=\sqrt{c^2+d^2}$$? Or whether $$a^2+b^2=c^2+d^2$$? (1) $$\frac{a}{b}=\frac{c}{d}$$ --> $$a=cx$$ and $$b=dx$$, for some non-zero $$x$$. Not sufficient. (2) $$\sqrt{a^2}+\sqrt{b^2}=\sqrt{c^2} +\sqrt{d^2}$$ --> $$|a|+|b|=|c|+|d|$$. Not sufficient. (1)+(2) From (1) $$a=cx$$ and $$b=dx$$, substitute this in (2): $$|cx|+|dx|=|c|+|d|$$ --> $$|x|(|c|+|d|)=|c|+|d|$$ --> $$|x|=1$$ (another solution $$|c|+|d|=0$$ is not possible as $$d$$ in (1) given in denominator and can not be zero, so $$d\neq{0}$$ --> $$|c|+|d|>0$$) --> now, as $$|x|=1$$ and $$a=cx$$ and $$b=dx$$, then $$|a|=|c|$$ and $$|b|=|d|$$ --> square this equations: $$a^2=c^2$$ and $$b^2=d^2$$ --> add them: $$a^2+b^2=c^2+d^2$$. Sufficient. Answer: C. I am getting a different final result for answer (C). Here is my approach: $$\sqrt{a^2} - \sqrt{d^2} = \sqrt{c^2} - \sqrt{b^2}$$ ----from statement (2) Squaring both sides $$a^2 + d^2 - 2\sqrt{a^2*d^2} = c^2 + b^2 - 2\sqrt{b^2*c^2}$$ from statement (1) we know that ad=bc --> a^2*d^2 = b^2*c^2 Cancelling last term of both sides, we get a^2 + d^2 = c^2 + b^2 Thus, a^2 - b^2 = c^2 - d^2 Not able to figure out where I went wrong. Please suggest! Thanks Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5536 Location: Pune, India Followers: 1366 Kudos [?]: 6950 [0], given: 178 Re: ManhttanGMAT Practice CAT [#permalink] 04 Jun 2012, 18:39 Expert's post kunalbh19 wrote: I am getting a different final result for answer (C). Here is my approach: $$\sqrt{a^2} - \sqrt{d^2} = \sqrt{c^2} - \sqrt{b^2}$$ ----from statement (2) Squaring both sides $$a^2 + d^2 - 2\sqrt{a^2*d^2} = c^2 + b^2 - 2\sqrt{b^2*c^2}$$ from statement (1) we know that ad=bc --> a^2*d^2 = b^2*c^2 Cancelling last term of both sides, we get a^2 + d^2 = c^2 + b^2 Thus, a^2 - b^2 = c^2 - d^2 Not able to figure out where I went wrong. Please suggest! Thanks There is nothing wrong with your approach. The relation you have got holds (a^2 - b^2 = c^2 - d^2). But if you start doing algebraic manipulations on the starting point without an eye on what you need to achieve at the end, you may not obtain the result you want. You can manipulate an expression in many ways to get seemingly different results. Notice that Bunuel got a^2 = c^2 and b^2 = d^2. He could have chosen to add them as a^2 + d^2 = c^2 + b^2 (or subtract them) which is same as your result. But he chose to add them as a^2 + b^2 = c^2 + d^2 to get the expression he desired. Using the same two expressions, Bunuel arrived at a^2 + b^2 = c^2 + d^2 and you arrived at a^2 - b^2 = c^2 - d^2, both of which are correct. But only one of them (a^2 + b^2 = c^2 + d^2) helps you answer the question directly since you know that the distance of a point (a, b) is given by square root of (a^2 + b^2). Try to find the relation between individual variables instead of working on the equations as a whole. Either use number plugging or Bunuel's algebraic approach. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Manager
Joined: 28 Dec 2012
Posts: 91
Location: India
Concentration: Strategy, Finance
GMAT 1: Q V
WE: Engineering (Energy and Utilities)
Followers: 2

Kudos [?]: 38 [0], given: 77

Re: In the rectangular coordinate system, are the points (a, b) [#permalink]  15 Jan 2013, 07:45
1+2:

1) Ensures that the lines joining each of the two points to origin have same slope.
2) Ensures that absicca and ordinates correspondingly have equal magnitudes.
{If one line has points (a,b) then the other line will have coordinates (ak,bk) but (2) ensures that |k| = 1.}

Hence C.

KUDOS IF YOU LIKE!
_________________

Impossibility is a relative concept!!

Senior Manager
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 307
Concentration: Accounting
GMAT Date: 04-06-2013
GPA: 3.65
Followers: 9

Kudos [?]: 164 [0], given: 46

Re: ManhttanGMAT Practice CAT [#permalink]  22 Apr 2013, 11:55
Bunuel wrote:
nsp007 wrote:
In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) $$\sqrt{a^2}+ \sqrt{b^2} = \sqrt{c^2} + \sqrt{d^2}$$

Will post OA later.

In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

Distance between the point A (x,y) and the origin can be found by the formula: $$D=\sqrt{x^2+y^2}$$.

So we are asked whether $$\sqrt{a^2+b^2}=\sqrt{c^2+d^2}$$? Or whether $$a^2+b^2=c^2+d^2$$?

(1) $$\frac{a}{b}=\frac{c}{d}$$ --> $$a=cx$$ and $$b=dx$$, for some non-zero $$x$$. Not sufficient.

(2) $$\sqrt{a^2}+\sqrt{b^2}=\sqrt{c^2} +\sqrt{d^2}$$ --> $$|a|+|b|=|c|+|d|$$. Not sufficient.

(1)+(2) From (1) $$a=cx$$ and $$b=dx$$, substitute this in (2): $$|cx|+|dx|=|c|+|d|$$ --> $$|x|(|c|+|d|)=|c|+|d|$$ --> $$|x|=1$$ (another solution $$|c|+|d|=0$$ is not possible as $$d$$ in (1) given in denominator and can not be zero, so $$d\neq{0}$$ --> $$|c|+|d|>0$$) --> now, as $$|x|=1$$ and $$a=cx$$ and $$b=dx$$, then $$|a|=|c|$$ and $$|b|=|d|$$ --> square this equations: $$a^2=c^2$$ and $$b^2=d^2$$ --> add them: $$a^2+b^2=c^2+d^2$$. Sufficient.

Hi Bunnel
i am not understanding how $$\sqrt{a^2}+\sqrt{b^2}=\sqrt{c^2} +\sqrt{d^2}$$ --> $$|a|+|b|=|c|+|d|$$
have come?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5536
Location: Pune, India
Followers: 1366

Kudos [?]: 6950 [0], given: 178

Re: ManhttanGMAT Practice CAT [#permalink]  22 Apr 2013, 21:00
Expert's post
mun23 wrote:
$$\sqrt{a^2}+\sqrt{b^2}=\sqrt{c^2} +\sqrt{d^2}$$ --> $$|a|+|b|=|c|+|d|$$
have come?

By convention, only positive roots are considered (at least in GMAT)

$$\sqrt{4} = 2$$ (and not -2)

Similarly, $$\sqrt{a^2} = |a|$$ i.e. only the positive value
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Manager
Joined: 04 Apr 2013
Posts: 153
Followers: 1

Kudos [?]: 30 [1] , given: 36

Re: coordinate geometry [#permalink]  15 Aug 2013, 18:29
1
KUDOS
sudharsansuski wrote:
In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) (a^2)^0.5 + (b^2)^0.5 = (c^2)^0.5 + (d^2)^0.5

Origin on coordinate system is (0,0). The question is if distance between (0,0) to (a,b) is same as distance between (0,0) to (c,d)

Case 1: - a/b = c/d

let a=7, b= 14 then a/b = 1/2.

So c/d fraction has to be 1/2. i.e. c can be 2 and d can be 4. or c can be 6 & d can be 12 or c can be 7 & d can be 14. So distance between origin can either be same to (c,d) or different from (a,b). Clearly insufficient

Case 2:- (a^2)^0.5 + (b^2)^0.5 = (c^2)^0.5 + (d^2)^0.5

translates to "a + b = c + d"

let (a,b) = (4,4) and (c,d) = (4,4). Then it satisfies the condition a+b = c+d. Also distance from origin to (a,b) is same as (c,d).

let (a,b) = (5,3) and (c,d) = (4,4). Then it satisfies the condition a+b = c+d. And distance from origin to (a,b) is not same as (c,d).

Insufficient.

Lets take 1 & 2 together

we have a/b = c/d.......so a= bc/d--- Eq (1)

we also have a + b = c + d

substitute a=bc/d from Eq(1)

bc/d + b = c + d

b(c/d + 1) = c + d

b(c + d) = d(c+d)

so b = d

similarly we get a=b.

so taking 1 & 2 together, the distance between origin to both points are equal.
_________________

MGMAT1 - 540 ( Trying to improve )

Current Student
Joined: 14 Dec 2012
Posts: 844
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Followers: 42

Kudos [?]: 740 [0], given: 197

Re: In the rectangular coordinate system, are the points (a, b) [#permalink]  16 Aug 2013, 02:33
sudharsansuski wrote:
In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) (a^2)^0.5 + (b^2)^0.5 = (c^2)^0.5 + (d^2)^0.5

basically we need to prove
$$a^2+b^2 = c^2+d^2$$

stmnt 1:
$$\frac{a}{b} = \frac{c}{d}$$

1/2 = 3/6 ==>using this we can prove NO
1/2 = 1/2 ==>using these numbers we can prove yes

hence insufficient
statement 2:
$$\sqrt{(a^2)} + \sqrt{(b^2)} = \sqrt{(c^2)} + \sqrt{(d^2)}$$or$$|a| + |b| = |c| + |d|$$

putting $$a=b=c=d=1$$..we will get YES.
Putting $$a= 1, b=2, c= 0, d=3$$...we will get NO.
HENCE INSUFFICIENT.

combining.
from 2nd statement: $$|a| + |b| = |c| + |d|$$
rearrange:
$$|a| - |d| = |c| - |b|$$ and then square both sides.
$$a^2 + d^2 - 2*|a|*|d| = c^2 + b^2 - 2*|c|*|b|.$$

Since $$ad = bc$$ as per statement 1
we can cancel few things:
$$a^2 + d^2 - 2*|a|*|d| = c^2 + b^2 - 2*|c|*|b|.$$

hence sufficient
_________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...

learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat- ... assessment

Intern
Joined: 30 May 2012
Posts: 21
Concentration: Finance, Strategy
GMAT 1: 730 Q49 V41
GPA: 3.39
Followers: 0

Kudos [?]: 5 [0], given: 0

Re: In the rectangular coordinate system, are the points (a, b) [#permalink]  16 Aug 2013, 08:13
nsp007 wrote:
In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) $$\frac{a}{b}=\frac{c}{d}$$

(2) $$\sqrt{a^2}+ \sqrt{b^2} = \sqrt{c^2} + \sqrt{d^2}$$

1. ad-bc=0 means that the vector pointing to (c,d) is a scalar multiple of the vector pointing to (a,b). In other words they are collinear with the origin. If they are equidistant to the origin, the scalar will be 1 or -1. But given this information it could be any scalar. Not sufficient.

2. |a|+|b|=|c|+|d|. This means that (a,b) and (c,d) both lay on some square centered at the origin. But they could be anywhere on the square. Not sufficient.

1 and 2. (a,b) and (c,d) are collinear with the origin and both lay on a square centered at the origin. Therefore they must be the same distance from the origin. Sufficient. C
Manager
Joined: 21 Sep 2012
Posts: 154
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
Followers: 1

Kudos [?]: 90 [0], given: 31

Re: In the rectangular coordinate system, are the points (a, b) [#permalink]  14 Jul 2014, 05:56
janxavier wrote:
In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) (a^2 + b^2)^(1/2) = (c^2 + d^2)^(1/2)

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Using distance formula, we can say that statement 2 is sufficient to answer that (a,b) and (c,d) are equidistant from Origin. Please check the OA posted.
Intern
Joined: 20 Jun 2014
Posts: 15
Location: United States
Concentration: Finance, Economics
GPA: 3.87
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: In the rectangular coordinate system, are the points (a, b) [#permalink]  31 Jul 2014, 04:33
This was my view:

You see immediately that both statements alone are not sufficient. So start evaluating the combination of both:

Statement A says that that the points are on the same line through the origin. Statement B says that the different "possible" points all have an equal distance to the x-axis, but also to the y-axis. Therefore, combining both options say that either (a,b) = (c,d) or (a,b) = (-c, -d). So equidistant from origin.
Intern
Joined: 09 Mar 2014
Posts: 5
GPA: 3.01
WE: General Management (Energy and Utilities)
Followers: 0

Kudos [?]: 0 [0], given: 6

Re: In the rectangular coordinate system, are the points (a, b) [#permalink]  06 Jan 2015, 22:12
Bunuel Sir,

I Didn't understand this:-

given a/b=c/d=cx/dx

(as the ratios are equal then there exist some for which d=cx and b=dx)
Math Expert
Joined: 02 Sep 2009
Posts: 27465
Followers: 4305

Kudos [?]: 42112 [0], given: 5957

Re: In the rectangular coordinate system, are the points (a, b) [#permalink]  07 Jan 2015, 06:07
Expert's post
manojpandey80 wrote:
Bunuel Sir,

I Didn't understand this:-

given a/b=c/d=cx/dx

(as the ratios are equal then there exist some for which d=cx and b=dx)

a/b = c/d = cx/dx

For example: 16/32 = 2/4 = (2*8)/(4*8).
_________________
Re: In the rectangular coordinate system, are the points (a, b)   [#permalink] 07 Jan 2015, 06:07
Similar topics Replies Last post
Similar
Topics:
In the rectangular coordinate system, are the points (a, b) 0 15 Aug 2013, 18:29
In the rectangular coordinate system, are the points (a, b) 5 15 Jul 2008, 17:51
In the rectangular coordinate system, are the points (a, b) 2 17 Dec 2007, 13:57
1 In the rectangular coordinate system, are the points (a, b) 4 10 Dec 2007, 15:44
In the rectangular coordinate system, are the points (a, b) 3 23 Aug 2007, 12:51
Display posts from previous: Sort by