GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 04 Aug 2020, 04:01

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

In the xy-coordinate plane, is point R equidistant from

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 172
In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 03 Dec 2012, 04:25
13
114
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (01:25) correct 38% (01:32) wrong based on 2753 sessions

HideShow timer Statistics

In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y = -3.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65785
In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 03 Dec 2012, 04:32
29
28
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

Look at the diagram below:

Image

Notice, that the green line (x=-1) is the perpendicular bisector of the line segment with endpoints (-3,-3) and (1,-3), thus ANY point on this line will be equidistant from points (-3,-3) and (1,-3).

(1) The x-coordinate of point R is -1 --> point R is on the green line. Sufficient.
(2) Point R lies on the line y = -3 --> point R may or may not be on the green line. Not sufficient.

Answer: A.

Attachment:
Equidistant points.png
Equidistant points.png [ 9.68 KiB | Viewed 38357 times ]

_________________
Most Helpful Community Reply
Manager
Manager
avatar
Joined: 13 Aug 2012
Posts: 86
In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 11 Aug 2014, 02:21
11
6
We have to find out whether \(R(x,y)\) is equidistant from the two points mentioned

Using the distance formula
\((x+3)^2+(y+3)^2 = (x-1)^2+(y+3)^2\)
\((x+3)^2 = (x-1)^2\)

So basically we have to prove whether \((x+3)^2 = (x-1)^2\)or not?

1)Substituting\(-1\) in the above equation \((x+3)^2 = (x-1)^2\) results in it being equal
Thus sufficient

2)\(y = -3\)wouldn't help us with this eqn:\((x+3)^2 = (x-1)^2\)
Thus insufficient

Ans is A
General Discussion
Manager
Manager
avatar
Joined: 21 Jan 2010
Posts: 228
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 13 May 2013, 19:17
2
2
Walkabout wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y = -3.


Any point that lie on the perpendicular bisector the line segment with extreme points (-3,-3) and (1,-3) will satisfy this condition. The perpendicular bisector of the line segment is x=-1.

1) this means the point lies on x=-1. Sufficient.
2) This may or may not lie in the middle. The point -1,-3 is the mid point of the line segment but their are other points on the line such as (-2,-3) which doesn't satisfy the requirements. Insufficient.

Hence A.
Manager
Manager
User avatar
B
Joined: 15 Mar 2015
Posts: 103
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 16 May 2015, 08:25
1
I got really scared seeing this question. But visualizing the coordinate plane made for a much simpler approach.

Once I got the two points mapped out it was obvious that point R had to be on X = -1.

I suppose this was possible because the two points had the same Y coordinates, which allowed for several a straight line at equidistance from the two points. Has anyone got any suggestions or Q's that involves points without this possibility? e.g. A=(1,0) B=(6,6)
_________________
I love being wrong. An incorrect answer offers an extraordinary opportunity to improve.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 17272
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 16 May 2015, 10:32
3
Hi MarkusKarl,

Most Geometry questions have a "visual" component to them, so drawing the "work" involved (the shapes, the graph, etc.) will almost always be beneficial - in that way, you can connect conceptual ideas to real-world examples. GMAT questions in general are almost all pattern-based, so if you find yourself 'stuck' conceptually, you have to think about the rules involved and simplify the logic.

In your example, you name two points that don't share an X or Y co-ordinate, but the concept involved in this prompt applies to your example as well. There WILL be a "line" of co-ordinates that are equidistant from the two points that you named (it's just that the "line" will be a diagonal line and will NOT involve any shared X or Y co-ordinates).

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 9256
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 15 Nov 2015, 09:51
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3)

(1) The x coordinate of point R is -1
(2) Point R lies on line y = -3.

We get a graph as below:
Attachment:
GCDS inhimanshu In the xy-coordinate plane (20151113).jpg
GCDS inhimanshu In the xy-coordinate plane (20151113).jpg [ 16.17 KiB | Viewed 12287 times ]


In other words, it is asking whether point R is in the same distance from (-3,-3) and (1,-3).
The line x=-1 is in the same distance from the points, so the x-coordinate of R has to be -1. So condition 1 is sufficient,
making the answer A.

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Manager
User avatar
S
Joined: 04 Dec 2016
Posts: 97
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 03 Feb 2017, 23:45
Bunuel wrote:
Kchaudhary wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3)?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y=-3.


Merging topics. Please refer to the discussion above.


Hi Bunnel, in statement 1, how can you consider that y-coordinate of R is 0?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65785
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 03 Feb 2017, 23:55
Kchaudhary wrote:
Bunuel wrote:
Kchaudhary wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3)?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y=-3.


Merging topics. Please refer to the discussion above.


Hi Bunnel, in statement 1, how can you consider that y-coordinate of R is 0?


The y-coordinate of R is not necessarily 0. The point is that since x-coordinate of R is -1, then R is on the green line, so no matter what is the y-coordinate, R will be equidistant from the given points.

Image
_________________
Manager
Manager
avatar
G
Joined: 12 Jun 2016
Posts: 198
Location: India
Concentration: Technology, Leadership
WE: Sales (Telecommunications)
GMAT ToolKit User
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 14 May 2017, 04:55
3
1
HI Kchaudhary,

Just adding to Bunuel's solution.

Even though the term perpendicular bisector is used, we can infer S1 is sufficient without knowing about it. A quick sketch of the Co-ordinate will be able to get us there.

Consider the attached image. In the Image I have taken an Arbitrary point R on the green line. Named the given two points as A and B. Also labelled O for easier understanding.

What is asked is - AR = BR?. If you notice - Point A, B and R form two Right angles at common point O. In these two Right angled triangle, two sides are equal. AO = AB = 2 (Follows from given co-ordinates) and OR is common to both Right triangles. So, it clearly follows that the third side of both right angles MUST be equal. Meaning AR = BR. This makes S1 sufficient.

I hope this helped :)


Kchaudhary wrote:
Bunuel wrote:
Kchaudhary wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3)?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y=-3.


Merging topics. Please refer to the discussion above.


Hi Bunnel, in statement 1, how can you consider that y-coordinate of R is 0?

Attachments

File comment: Named given point A and B for clarity. Assumed Point R on green line
Equidistant points.png
Equidistant points.png [ 18.45 KiB | Viewed 25631 times ]


_________________
My Best is yet to come!
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 9256
GMAT 1: 760 Q51 V42
GPA: 3.82
In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 14 May 2017, 09:43
Walkabout wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y = -3.


Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

From the original condition, we can set up as this question as follows.
The distance between \(R(x,y)\) and \((-3,-3)\) is \(\sqrt{(x+3)^2 + (y+3)^2}\) and the distance between \(R(x,y)\) and \((1,-3)\) is \(\sqrt{(x-1)^2 + (y+3)^2}\).
Thus, we have \(\sqrt{(x+3)^2 + (y+3)^2} = \sqrt{(x-1)^2 + (y+3)^2}\).
Then \(x^2 + 6x + 9 + y^2 + 6y + 9 = x^2 -2x + 1 + y^2 + 6y + 9\).
\(6x + 9 = -2x + 1\)
\(8x = -8\)
\(x = -1\)

We have 2 variables \(x\) and \(y\) and 1 equation, \(x = -1\).
In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.

For 1), \(x = -1\), which is equivalent to the condition from the original question. No additional condition is provided. Thus this is not sufficient.

For 2), \(y = -3\). Then the point R is (-1,-3). This is sufficient.

Therefore, the answer is B.

-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4987
Location: Canada
GMAT 1: 770 Q49 V46
In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 08 Aug 2017, 08:10
5
Top Contributor
Walkabout wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y = -3.


Target question: Is point R equidistant from points (-3,-3) and (1,-3)?
This question is a great candidate for rephrasing the target question.

First sketch the two given points
Image

Notice that the point (-1, -3) is equidistant from the two given points. MORE IMPORTANTLY, every point on the line x = -1 is equidistant from the two given points.
Image

So, we can rephrase the target question . . .
REPHRASED target question: Is point R on the line x = -1?

Statement 1: The x coordinate of point R is -1
If the x-coordinate is -1, then point R is definitely on the line x = -1
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: Point R lies on the line y= -3
This tells us nothing about whether or not point R is on the line x = -1?
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer:

RELATED VIDEO

_________________
If you enjoy my solutions, you'll love my GMAT prep course.

Image
Director
Director
avatar
D
Joined: 01 Mar 2019
Posts: 586
Location: India
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 580 Q48 V21
GPA: 4
Reviews Badge
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 19 May 2019, 21:05
Bunuel wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

Look at the diagram below:

Image

Notice, that the green line (x=-1) is the perpendicular bisector of the line segment with endpoints (-3,-3) and (1,-3), thus ANY point on this line will be equidistant from points (-3,-3) and (1,-3).

(1) The x-coordinate of point R is -1 --> point R is on the green line. Sufficient.
(2) Point R lies on the line y = -3 --> point R may or may not be on the green line. Not sufficient.

Answer: A.

Attachment:
Equidistant points.png







Here in Statement(2),Point R lies on the line y = -3 then the only point on this line y=-3 equidistant from points is (-1,-3),.....so why not D?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65785
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 19 May 2019, 21:48
madgmat2019 wrote:
Bunuel wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

Look at the diagram below:

Image

Notice, that the green line (x=-1) is the perpendicular bisector of the line segment with endpoints (-3,-3) and (1,-3), thus ANY point on this line will be equidistant from points (-3,-3) and (1,-3).

(1) The x-coordinate of point R is -1 --> point R is on the green line. Sufficient.
(2) Point R lies on the line y = -3 --> point R may or may not be on the green line. Not sufficient.

Answer: A.

Attachment:
Equidistant points.png







Here in Statement(2),Point R lies on the line y = -3 then the only point on this line y=-3 equidistant from points is (-1,-3),.....so why not D?


From (2) point R can be ANY point on the line y = -3. If it's (-1, -3), then yes, R would be equidistant from points (-3,-3) and (1,-3) but if x-coordinate of point R is anything but -1, then R would NOT be equidistant from points (-3,-3) and (1,-3). For example, (-2, -3), (-1101, -3), ...
_________________
CEO
CEO
User avatar
V
Joined: 03 Jun 2019
Posts: 3339
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Reviews Badge CAT Tests
Re: In the xy-coordinate plane, is point R equidistant from  [#permalink]

Show Tags

New post 17 Aug 2019, 23:30
2
Walkabout wrote:
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

(1) The x-coordinate of point R is -1.
(2) Point R lies on the line y = -3.


Asked: In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

Let the co-ordinates of R be (x,y)

(1) The x-coordinate of point R is -1.
x=-1
Distance of R(-1,y) from point (-3,-3) \(= \sqrt{2^2 + (y+3)^2}\)
Distance of R(-1,y) from point (1,-3) \(= \sqrt{2^2 + (y+3)^2}\)
Point R equidistant from points (-3,-3) and (1,-3)
SUFFICIENT

(2) Point R lies on the line y = -3.
y=-3
Distance of R(-1,y) from point (-3,-3) \(= \sqrt{(x+3)^2}=|x+3|\)
Distance of R(-1,y) from point (1,-3) \(= \sqrt{(x-1)^2}=|x-1|\)
Point R is NOT NECESSARILY equidistant from points (-3,-3) and (1,-3)
NOT SUFFICIENT

IMO A
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
GMAT Club Bot
Re: In the xy-coordinate plane, is point R equidistant from   [#permalink] 17 Aug 2019, 23:30

In the xy-coordinate plane, is point R equidistant from

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne