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# What are the coordinates of the point A?

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Math Expert
Joined: 02 Sep 2009
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What are the coordinates of the point A?  [#permalink]

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23 Jul 2015, 02:57
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10
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Difficulty:

45% (medium)

Question Stats:

57% (01:11) correct 43% (01:20) wrong based on 188 sessions

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What are the coordinates of the point A?

(1) A is 2 units away from (3, 4).
(2) A is 3 units away from (0, 0).

Kudos for a correct solution.

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What are the coordinates of the point A?  [#permalink]

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23 Jul 2015, 03:04
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Bunuel wrote:
What are the coordinates of the point A?

(1) A is 2 units away from (3, 4).
(2) A is 3 units away from (0, 0).

Kudos for a correct solution.

Statement 1: A is 2 units away from (3, 4).
A can be anywhere on the circumference of a circle centered (3, 5) with Radius of 2 units, Hence
NOT SUFFICIENT

Statement 2: A is 3 units away from (0, 0)
A can be anywhere on the circumference of a circle centered (0, 0) with Radius of 3d units, Hence
NOT SUFFICIENT

Combining the two statements
There will be One point of Intersection of Circles drawn by the two statements (As shown in figure), hence
SUFFICIENT

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Re: What are the coordinates of the point A?  [#permalink]

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23 Jul 2015, 04:33
Bunuel wrote:
What are the coordinates of the point A?

(1) A is 2 units away from (3, 4).
(2) A is 3 units away from (0, 0).

Kudos for a correct solution.

A=(x,y) = ?

Per statement 1, coordinates at a distance of 2 units from (3,4) lie on the circumference of a circle with center (3,4) and radius 2 units. Thus all the points on the circumference of this circle can be A's coordinates. Thus this statement is not sufficient.

Per statement 2, coordinates at a distance of 3 units from (0,0) lie on the circumference of a circle with center (0,0) and radius 3 units. Thus all the points on the circumference of this circle can be A's coordinates. Thus this statement is not sufficient.

Combining, we see that the radii of the circles = 2+3 = 5 = distance between the centers of the 2 circles (= ((3-0)^2+)4-0)^2)^0.5) ----> The circles intersect each other at only 1 point. Thus we get a unique coordinate value for A---> C is the correct answer.
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Re: What are the coordinates of the point A?  [#permalink]

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23 Jul 2015, 07:26
Option C is Correct

As both the equation of circle makes the 3,4,5 triangle we can calculate the Point A
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Re: What are the coordinates of the point A?  [#permalink]

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26 Jul 2015, 12:47
Bunuel wrote:
What are the coordinates of the point A?

(1) A is 2 units away from (3, 4).
(2) A is 3 units away from (0, 0).

Kudos for a correct solution.

800score Official Solution:

All the points that lie at some specific distance from a given one are situated on the circle, which center is the given point and the radius is the distance. Therefore each statement by itself defines a circle (infinitely many points). So each statement by itself is NOT sufficient.

If we use the both statements together, we have two circles. Point A belongs to each one of them. Two circles can cross each other in one or two points. (Two circles can also have no common points at all, but it is NOT our case). The distance between the centers, (0, 0) and (3, 4), is √(3² + 4²) = √25 = 5. It equals to the sum of the radii, 2 + 3 = 5. Therefore the circles touch each other (cross) in exactly ONE point. Clearly, the coordinates of this point can be found by solving the system of the two equations of the circles. However we do NOT need to actually calculate the coordinates.

Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient.

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Re: What are the coordinates of the point A?  [#permalink]

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24 Mar 2018, 06:01
Hi in case if I would like to know how to calculate the coordinates of point A then how can I find assuming PS question

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Re: What are the coordinates of the point A?  [#permalink]

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24 Mar 2018, 10:59
kaushiksamrat wrote:
Hi in case if I would like to know how to calculate the coordinates of point A then how can I find assuming PS question

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Hello

If its a PS question with 5 options, we could also go option by option and check which option satisfies both the things: i.e., the point given in that option should be 2 units away from (3,4) and 3 units away from (0,0). We could use distance formula to check via options, that would probably help in getting to the answer faster.
Re: What are the coordinates of the point A?   [#permalink] 24 Mar 2018, 10:59
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