(x,y) co-ordinates of point A

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Nov 23, 2013 4:47 pm

Hello,

Can you please assist with this:

Point C's (x,y) coordinates are (2,1). Point B's (x,y) coordinates are (5,2).
Point A is the third vertex of triangle ABC, what are the (x,y) coordinates of
point A?

(1) Line segment AB has length 2.
(2) Line segment AC has length 2.

OA: E

Thanks a lot - Sri

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Source: Beat The GMAT — Data Sufficiency | Sat Nov 23, 2013 4:47 pm

Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Sat Nov 23, 2013 5:51 pm

Sri,
We Know Two points of a triangle,
Point C = (2,1) and Point B = (5,2)
Draw the x-y Lines accordingly and place the points.

To find Point A co-ordinates.

Statement 1: Line segment AB has length 2.
It says the distance between A and B is 2.
So point A can be either on top or below or to left or right of the Point B.
We can't say the Co-ordinates.Insufficient.

Statement 2 : Line segment AC has length 2.
Similarly it say only about the distance between A and C. Hence Insufficient.

Combining 1 and 2 : We can say the Point A is Equal distance from B and C. So, it should be between B and C. But We don't know whether it is on top or below both the points.
Hence Insufficient.

Answer is E

Regards,
Uva.

Known is a drop Unknown is an Ocean

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sun Nov 24, 2013 11:14 am

Uva@90 wrote:Sri,
We Know Two points of a triangle,
Point C = (2,1) and Point B = (5,2)
Draw the x-y Lines accordingly and place the points.

To find Point A co-ordinates.

Statement 1: Line segment AB has length 2.
It says the distance between A and B is 2.
So point A can be either on top or below or to left or right of the Point B.
We can't say the Co-ordinates.Insufficient.

Statement 2 : Line segment AC has length 2.
Similarly it say only about the distance between A and C. Hence Insufficient.

Combining 1 and 2 : We can say the Point A is Equal distance from B and C. So, it should be between B and C. But We don't know whether it is on top or below both the points.
Hence Insufficient.

Answer is E

Regards,
Uva.

Hello Uva,

Thanks for your reply. Can you please tell me how to calculate the length of a line segment? I was just trying to find out what co-ordinates for A would satisfy the condition that line segment AB has length 2. Thanks for your help.

Best Regards,
Sri

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GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Nov 24, 2013 6:04 pm

Hi Sri,

If you're looking at a DIAGONAL line segment on a graph, then you can draw a right triangle based on that diagonal line as the HYPOTENEUSE. Now you can use the Pythagorean Theorem (A^2 + B^2 = C^2) to calculate the length of the diagonal line.

In answer to your other question, once we know that point B is at (5,2), and that segment AB = 2, then point A could be "2 away" from B in ANY DIRECTION. If you were to draw this, then you would have a circle (of radius 2) around point B. This would account for ALL the possible positions for point A.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Mon Nov 25, 2013 7:22 am

gmattesttaker2 wrote:
Uva@90 wrote:Sri,
We Know Two points of a triangle,
Point C = (2,1) and Point B = (5,2)
Draw the x-y Lines accordingly and place the points.

To find Point A co-ordinates.

Statement 1: Line segment AB has length 2.
It says the distance between A and B is 2.
So point A can be either on top or below or to left or right of the Point B.
We can't say the Co-ordinates.Insufficient.

Statement 2 : Line segment AC has length 2.
Similarly it say only about the distance between A and C. Hence Insufficient.

Combining 1 and 2 : We can say the Point A is Equal distance from B and C. So, it should be between B and C. But We don't know whether it is on top or below both the points.
Hence Insufficient.

Answer is E

Regards,
Uva.
Hello Uva,

Thanks for your reply. Can you please tell me how to calculate the length of a line segment? I was just trying to find out what co-ordinates for A would satisfy the condition that line segment AB has length 2. Thanks for your help.

Best Regards,
Sri

Sri,
Rich has mentioned a point.

It is measured using sqrt[(x2-x1)^2 +(y2-y1)^2]

for |AB|= 2 where B = (5,2)

sqrt[(5-x1)^2 + (2-y1)^2 ] =2
from this we need to find Point A=(x1,y1).

Hope it helps you.

Regards,
Uva.

Known is a drop Unknown is an Ocean

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Nov 30, 2013 1:22 pm

Uva@90 wrote:
gmattesttaker2 wrote:
Uva@90 wrote:Sri,
We Know Two points of a triangle,
Point C = (2,1) and Point B = (5,2)
Draw the x-y Lines accordingly and place the points.

To find Point A co-ordinates.

Statement 1: Line segment AB has length 2.
It says the distance between A and B is 2.
So point A can be either on top or below or to left or right of the Point B.
We can't say the Co-ordinates.Insufficient.

Statement 2 : Line segment AC has length 2.
Similarly it say only about the distance between A and C. Hence Insufficient.

Combining 1 and 2 : We can say the Point A is Equal distance from B and C. So, it should be between B and C. But We don't know whether it is on top or below both the points.
Hence Insufficient.

Answer is E

Regards,
Uva.
Hello Uva,

Thanks for your reply. Can you please tell me how to calculate the length of a line segment? I was just trying to find out what co-ordinates for A would satisfy the condition that line segment AB has length 2. Thanks for your help.

Best Regards,
Sri
Sri,
Rich has mentioned a point.

It is measured using sqrt[(x2-x1)^2 +(y2-y1)^2]

for |AB|= 2 where B = (5,2)

sqrt[(5-x1)^2 + (2-y1)^2 ] =2
from this we need to find Point A=(x1,y1).

Hope it helps you.

Regards,
Uva.

Hello Uva,

I was just wondering for what situation would be answer be C. i.e. when would it happen that A will have exactly 1 (x,y) co-ordinate. I am thinking that if the question were to say :

(1) Line segment AB has length 3.
(2) Line segment AC has length 1.

it might be C.

Can you please share your thoughts on this? Thanks for all your valuable time and help.

Best Regards,
Sri

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Nov 30, 2013 4:13 pm

Hi Sri,

Your theoretical example actually INCREASES the number of potential co-ordinates that could be the answer. Here's why.

In the original prompt, the two Facts state that the two line segments both have a length of 2. So the third co-ordinate of the triangle could be "above" the diagonal line or "below" it. In effect, you'd have a mirror-image of an isosceles triangle and there are 2 potential locations for the third co-ordinate.

With your example, the two Facts give us line segments of 1 and 3. So the third co-ordinate might be closer to EITHER of the other co-ordinates AND it might be mirror-imaged "above" the line or "below" it. This scenario creates 4 potential locations for the third co-ordinate. It would still be INSUFFICIENT (E).

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Nov 30, 2013 4:57 pm

[email protected] wrote:Hi Sri,

Your theoretical example actually INCREASES the number of potential co-ordinates that could be the answer. Here's why.

In the original prompt, the two Facts state that the two line segments both have a length of 2. So the third co-ordinate of the triangle could be "above" the diagonal line or "below" it. In effect, you'd have a mirror-image of an isosceles triangle and there are 2 potential locations for the third co-ordinate.

With your example, the two Facts give us line segments of 1 and 3. So the third co-ordinate might be closer to EITHER of the other co-ordinates AND it might be mirror-imaged "above" the line or "below" it. This scenario creates 4 potential locations for the third co-ordinate. It would still be INSUFFICIENT (E).

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

Thanks for the explanation. I was not clear with the following though:

So the third co-ordinate of the triangle could be "above" the diagonal line or "below" it.

I was not clear how this diagonal will be formed. Can you please explain? Thanks a lot.

Best Regards,
Sri

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