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 350,000 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:

On the coordinate plane , points P and Q are defined by the [#permalink]
14 Aug 2013, 13:45

2

This post received KUDOS

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

69% (03:11) correct
31% (02:34) wrong based on 108 sessions

On the coordinate plane , points P and Q are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?

Re: On the coordinate plane , points P and Q are defined by the [#permalink]
14 Aug 2013, 16:18

1

This post received KUDOS

Asifpirlo wrote:

On the coordinate plane , points P and Q are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?

Re: On the coordinate plane , points P and Q are defined by the [#permalink]
14 Aug 2013, 19:37

3

This post received KUDOS

Asifpirlo wrote:

On the coordinate plane , points P and Q are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?

since area = πr^2 = (25/4) π==>\(r = \frac{5}{2}\) ==>diameter =\(5\) ........(1

now see diag Point A\((-1,0)\) AND C \((3,3)\) Draw perpendicular from C to X-AXIS at\(B (0,3)\) therefore ABC is right triangle with angle\(B = 90\) clearl \(AB = 4\) , \(BC = 3\)==>according to pythogoras theorem\(AC = 5\) (diameter of circle) so chord \(AC\) is actually diameter...hence mid point of \(AC\) will be centre. mid point = (avg of x co-ordinates , avg of y co-ordinate) hence mid point co-ordinate will be \((\frac{(3-1)}{2} ,\frac{(3+0)}{2}) = (1,1.5)\)

hence D

Attachments

Untitled.png [ 11.45 KiB | Viewed 1287 times ]

_________________

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

Re: On the coordinate plane , points P and Q are defined by the [#permalink]
14 Aug 2013, 22:25

3

This post received KUDOS

An alternative way to approach this problem would be to calculate the distance between the center point and the other two points mentioned in the problem. The distance between center point and other two given points should be the same (will be radius) . Distance between two points can be calculated as square root of ((x2-x1)^2+(y2-y1)^2))

Option -1: Distance 1 is √(6.25+1 )=√7.25 , Distance 2 is √(2.25+4)=√6.25.Hence Incorrect. Option-2: Distance1 is √(9+25 )=√34 , Distance 2 is √(1+64)=√65.Hence Incorrect. Option-3: Distance1 is √(1+0 )=√1 , Distance 2 is √(9+9)=√18.Hence Incorrect. Option-2: Distance1 is √(4+2.25)=√6.25 , Distance 2 is √(4+2.25)=√6.25. Both are equal and hence Correct. Option-2: Distance1 is √(9+4 )=√13 , Distance 2 is √(1+1)=√2. Hence Incorrect.

Re: On the coordinate plane , points P and Q are defined by the [#permalink]
15 Aug 2013, 02:16

Asifpirlo wrote:

On the coordinate plane , points P and Q are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?

Re: On the coordinate plane , points P and Q are defined by the [#permalink]
25 Aug 2013, 05:41

I m sorry to ask this question.. I am new to GMAT, you may find this question silly but still I cant able to get this. We have a point on the circle(x,y)=(-1,0) and we have radius r=5/2. Equation of circle is : (x-a)^2+(y-b)^2 = r^2. By simply substituting above (x,y) and r we can find (a,b) which is the center. Y WE ARE GETTING 2 EQUATIONS(as done by maaadhu) SOLVING IT TO GET A FINAL EQUATION AND THEN SUBSTITUTING ANSWER OPTIONS AND SEEING? _________________

Re: On the coordinate plane , points P and Q are defined by the [#permalink]
25 Aug 2013, 09:38

1

This post received KUDOS

Expert's post

shivananthraj wrote:

I m sorry to ask this question.. I am new to GMAT, you may find this question silly but still I cant able to get this. We have a point on the circle(x,y)=(-1,0) and we have radius r=5/2. Equation of circle is : (x-a)^2+(y-b)^2 = r^2. By simply substituting above (x,y) and r we can find (a,b) which is the center. Y WE ARE GETTING 2 EQUATIONS(as done by maaadhu) SOLVING IT TO GET A FINAL EQUATION AND THEN SUBSTITUTING ANSWER OPTIONS AND SEEING?

The approach you are talking about allows to get the answer without actually solving the equations.

BTW, how can you solve (-1-a)^2+(0-b)^2 = (5/2)^2 for a and b? _________________

Re: On the coordinate plane , points P and Q are defined by the [#permalink]
25 Aug 2013, 14:24

1

This post received KUDOS

shivananthraj wrote:

I m sorry to ask this question.. I am new to GMAT, you may find this question silly but still I cant able to get this. We have a point on the circle(x,y)=(-1,0) and we have radius r=5/2. Equation of circle is : (x-a)^2+(y-b)^2 = r^2. By simply substituting above (x,y) and r we can find (a,b) which is the center. Y WE ARE GETTING 2 EQUATIONS(as done by maaadhu) SOLVING IT TO GET A FINAL EQUATION AND THEN SUBSTITUTING ANSWER OPTIONS AND SEEING?

Yes brother you can back solve it from the last equation you got... but evaluating the reals roots of the equation will be cumbersome.......

Indeed you can solve any gmat problem without applying some formulas ,And just with few basic understandings. _________________

Re: On the coordinate plane , points P and Q are defined by the [#permalink]
24 Apr 2015, 12:54

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: On the coordinate plane , points P and Q are defined by the [#permalink]
24 Apr 2015, 13:26

Asifpirlo wrote:

On the coordinate plane , points P and Q are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?

Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.

One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).

Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PQ is the diameter of the circle.

There can be a case when PQ is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.

If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans.

Re: On the coordinate plane , points P and Q are defined by the [#permalink]
27 Apr 2015, 04:02

1

This post received KUDOS

Expert's post

nailgmat2015 wrote:

Asifpirlo wrote:

On the coordinate plane , points P and Q are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?

Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.

One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).

Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PQ is the diameter of the circle.

There can be a case when PQ is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.

If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans.

Please note that every line passing through centre of the circle does not bisect the chord. Only the line which passes through the centre and is perpendicular to the chord bisects the chord. For example refer the diagram below. In this diagram there are various lines which pass through the centre and intersect the chord, but only OD will bisect the chord as it is perpendicular to the chord.

For this question, you got the right answer as you assumed PQ to be the diameter which is actually the case. A better method for this question would have been:

Step-I Find the radius of the circle from the given area of the circle which gives us radius = 2.5 and hence diameter = 5

Step-II In this case, we can observe that the length of the chord PQ is 5( by using the distance formula). Since the length of chord PQ is equal to the length of the diameter that would mean that PQ is the diameter of the circle. Since PQ is the diameter of the circle, the midpoint of PQ would be the centre of the circle which gives us the coordinates of centre as (1, 1.5)

Re: On the coordinate plane , points P and Q are defined by the [#permalink]
27 Apr 2015, 04:48

EgmatQuantExpert wrote:

nailgmat2015 wrote:

Asifpirlo wrote:

On the coordinate plane , points P and Q are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?

Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.

One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).

Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PQ is the diameter of the circle.

There can be a case when PQ is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.

If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans.

Please note that every line passing through centre of the circle does not bisect the chord. Only the line which passes through the centre and is perpendicular to the chord bisects the chord. For example refer the diagram below. In this diagram there are various lines which pass through the centre and intersect the chord, but only OD will bisect the chord as it is perpendicular to the chord.

For this question, you got the right answer as you assumed PQ to be the diameter which is actually the case. A better method for this question would have been:

Step-I Find the radius of the circle from the given area of the circle which gives us radius = 2.5 and hence diameter = 5

Step-II In this case, we can observe that the length of the chord PQ is 5( by using the distance formula). Since the length of chord PQ is equal to the length of the diameter that would mean that PQ is the diameter of the circle. Since PQ is the diameter of the circle, the midpoint of PQ would be the centre of the circle which gives us the coordinates of centre as (1, 1.5)

Hope its clear

Regards Harsh

Hi harsh,

Thanks for such a wonderful explanation. I guess I need to brush up my basics once.

Thanks, R

gmatclubot

Re: On the coordinate plane , points P and Q are defined by the
[#permalink]
27 Apr 2015, 04:48

Originally posted on MIT Sloan School of Management : We are busy putting the final touches on our application. We plan to have it go live by July 15...