It is currently 23 Nov 2017, 06:33

### 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 xy-coordinate plane, is point R equidistant from

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178

Kudos [?]: 3591 [0], given: 0

In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

03 Dec 2012, 05:25
43
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

58% (01:07) correct 42% (01:16) wrong based on 1681 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.
[Reveal] Spoiler: OA

Kudos [?]: 3591 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42326

Kudos [?]: 133109 [7], given: 12412

In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

03 Dec 2012, 05:32
7
KUDOS
Expert's post
18
This post was
BOOKMARKED
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

Look at the diagram below:

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.

[Reveal] Spoiler:
Attachment:

Equidistant points.png [ 9.68 KiB | Viewed 14324 times ]

_________________

Kudos [?]: 133109 [7], given: 12412

Senior Manager
Joined: 21 Jan 2010
Posts: 329

Kudos [?]: 229 [1], given: 12

Re: In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

13 May 2013, 20:17
1
KUDOS
1
This post was
BOOKMARKED
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.

Kudos [?]: 229 [1], given: 12

Intern
Joined: 04 Jun 2014
Posts: 48

Kudos [?]: 3 [0], given: 5

Re: In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

06 Aug 2014, 05:30
Why does the green line go through point -1 ? I couldn't find any chapter which explains this system.. can anyone help?

Kudos [?]: 3 [0], given: 5

Manager
Joined: 13 Aug 2012
Posts: 114

Kudos [?]: 94 [3], given: 118

In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

11 Aug 2014, 03:21
3
KUDOS
3
This post was
BOOKMARKED
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

Kudos [?]: 94 [3], given: 118

Manager
Joined: 15 Mar 2015
Posts: 113

Kudos [?]: 29 [0], given: 7

Re: In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

16 May 2015, 09:25
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.

Kudos [?]: 29 [0], given: 7

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10169

Kudos [?]: 3536 [1], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

16 May 2015, 11:32
1
KUDOS
Expert's post
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
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3536 [1], given: 173

Intern
Joined: 04 Dec 2016
Posts: 8

Kudos [?]: [0], given: 41

Re: In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

04 Feb 2017, 00:45
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?

Kudos [?]: [0], given: 41

Math Expert
Joined: 02 Sep 2009
Posts: 42326

Kudos [?]: 133109 [0], given: 12412

Re: In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

04 Feb 2017, 00:55
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.

_________________

Kudos [?]: 133109 [0], given: 12412

Manager
Joined: 12 Jun 2016
Posts: 229

Kudos [?]: 42 [0], given: 145

Location: India
WE: Sales (Telecommunications)
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

14 May 2017, 05:10
Hi lou34,

Thats because S1 says so.

S1 says - The X-co-ordinate of Point R is -1. This mean it will have to R WILL have to be ANY point on the green line mentioned by Bunuel.

I hope this clears your question.

lou34 wrote:
Why does the green line go through point -1 ? I couldn't find any chapter which explains this system.. can anyone help?

_________________

My Best is yet to come!

Kudos [?]: 42 [0], given: 145

Manager
Joined: 12 Jun 2016
Posts: 229

Kudos [?]: 42 [0], given: 145

Location: India
WE: Sales (Telecommunications)
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

14 May 2017, 05:55
HI Kchaudhary,

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 [ 18.45 KiB | Viewed 3383 times ]

_________________

My Best is yet to come!

Kudos [?]: 42 [0], given: 145

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4354

Kudos [?]: 3058 [0], given: 0

GPA: 3.82
In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

14 May 2017, 10:43
Expert's post
1
This post was
BOOKMARKED
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.

-> 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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Kudos [?]: 3058 [0], given: 0

Manager
Joined: 09 Jan 2016
Posts: 134

Kudos [?]: 92 [0], given: 59

GPA: 3.4
WE: General Management (Human Resources)
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

10 Jul 2017, 08:04
MathRevolution 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 $$x^2 + 6x + 9 + y^2 + 6y + 9 = x^2 -2x + 1 + y^2 + 6y + 9$$.
$$6x + 9 = -2x + 1$$
$$8x = -8$$
Got...methodical way.
$$x = -1$$

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.

-> 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.
Got it..methodical way.

Kudos [?]: 92 [0], given: 59

SVP
Joined: 12 Sep 2015
Posts: 1851

Kudos [?]: 2625 [0], given: 362

Re: In the xy-coordinate plane, is point R equidistant from [#permalink]

### Show Tags

08 Aug 2017, 09:10
Expert's post
Top Contributor
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

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.

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

[Reveal] Spoiler:
A

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2625 [0], given: 362

Re: In the xy-coordinate plane, is point R equidistant from   [#permalink] 08 Aug 2017, 09:10
Display posts from previous: Sort by