Last visit was: 14 Aug 2024, 23:25 It is currently 14 Aug 2024, 23:25
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 02 Dec 2012
Posts: 172
Own Kudos [?]: 24706 [290]
Given Kudos: 29
Math Expert
Joined: 02 Sep 2009
Posts: 94944
Own Kudos [?]: 649655 [97]
Given Kudos: 86941
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 31013 [8]
Given Kudos: 799
General Discussion
Manager
Joined: 21 Jan 2010
Posts: 193
Own Kudos [?]: 617 [6]
Given Kudos: 12
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
3
Kudos
3
Bookmarks
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
Joined: 15 Mar 2015
Posts: 89
Own Kudos [?]: 64 [1]
Given Kudos: 7
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
1
Kudos
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)
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11831 [4]
Given Kudos: 450
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]
3
Kudos
1
Bookmarks
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
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17161 [4]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
2
Kudos
2
Bookmarks
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 [ 16.17 KiB | Viewed 51016 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,

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
Manager
Joined: 04 Dec 2016
Posts: 59
Own Kudos [?]: 67 [1]
Given Kudos: 52
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
1
Kudos
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?
Manager
Joined: 12 Jun 2016
Posts: 145
Own Kudos [?]: 233 [6]
Given Kudos: 151
Location: India
WE:Sales (Telecommunications)
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
5
Kudos
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 63668 times ]

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17161 [4]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
In the xy-coordinate plane, is point R equidistant from [#permalink]
2
Kudos
2
Bookmarks
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.
Director
Joined: 01 Mar 2019
Posts: 591
Own Kudos [?]: 525 [0]
Given Kudos: 207
Location: India
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 580 Q48 V21
GPA: 4
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
Bunuel wrote:
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.

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
Joined: 02 Sep 2009
Posts: 94944
Own Kudos [?]: 649655 [0]
Given Kudos: 86941
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
Bunuel wrote:
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.

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), ...
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5332
Own Kudos [?]: 4294 [5]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
5
Kudos
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
Intern
Joined: 16 Feb 2021
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 0
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
Hello,
In this question I have new dimension to think about

What happens if statement 2 not sufficient but if statement 1 is sufficient and also statement 1 & 2 also sufficient.
In this case, which option to be best possible solution.

Like in this case statement 1 is sufficient
and also statement 1 and 2 is sufficient as statement 1 suggest that x coordinate is -1 and statement 2 suggest that point R lie on the y=-3. The coordinate is (-1, -3) which is also equidistant and hence sufficient.
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11831 [1]
Given Kudos: 450
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]
1
Kudos
Hi amiteshiitr,

In DS, the 5 answers choices are always the same 5 options. If you find that either Fact 1 or Fact 2 is Sufficient on its own, then you do NOT need any additional information to answer the question, so Answer C (re: "Together") will not be the correct answer.

Based on your example: Fact 1 is Sufficient; Fact 2 is Insufficient - the final Answer would be Answer A.

GMAT assassins aren't born, they're made,
Rich
VP
Joined: 11 Aug 2020
Posts: 1242
Own Kudos [?]: 210 [0]
Given Kudos: 332
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
Bunuel wrote:
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.

Attachment:
Equidistant points.png

Great post. I assume this applies in all cases when you have a perpendicular bisector?
Math Expert
Joined: 02 Sep 2009
Posts: 94944
Own Kudos [?]: 649655 [0]
Given Kudos: 86941
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
CEdward wrote:
Bunuel wrote:
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.

Attachment:
Equidistant points.png

Great post. I assume this applies in all cases when you have a perpendicular bisector?

Yes. Any point on a perpendicular bisector of a segment is equidistant from endpoints of this segment.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19311
Own Kudos [?]: 22921 [1]
Given Kudos: 286
Location: United States (CA)
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
1
Kudos
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.

Solution:

Question Stem Analysis:

We need to determine whether point R is equidistant from points (-3,-3) and (1,-3), If it is, then it must be on the perpendicular bisector of the segment connecting (-3,-3) and (1,-3). Since the segment connecting (-3,-3) and (1,-3) is horizontal, the perpendicular bisector of the segment must be vertical, passing through the midpoint of the segment. Since the midpoint of the segment is (-1, -3), the equation of the perpendicular bisector is x = -1. That is, if R is any point on the line x = -1, then it’s equidistant from points (-3,-3) and (1,-3).

Statement One Alone:

Since the x-coordinate of point R is -1, R must be a point on the line x = -1. Therefore, it is equidistant from points (-3,-3) and (1,-3). Statement one alone is sufficient.

Statement Two Alone:

We see that R is a point on the line containing the segment connecting (-3,-3) and (1,-3). However, we can’t determine whether it is equidistant from points (-3,-3) and (1,-3). For example, if R = (-1, -3), i.e., the midpoint of (-3,-3) and (1,-3), then it is equidistant from points (-3,-3) and (1,-3). Otherwise, it is not. Statement two alone is not sufficient.

GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6057
Own Kudos [?]: 13956 [3]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
2
Kudos
1
Bookmarks
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.

Solve the Official Questions more productively

Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
and Dedicated Data Sufficiency (DS) Course

Video solution by GMATinsight

Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub
Tutor
Joined: 17 Jul 2019
Posts: 1303
Own Kudos [?]: 1759 [0]
Given Kudos: 66