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# In the xy-coordinate system, the distance between points

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
In the xy-coordinate system, the distance between points  [#permalink]

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26 Mar 2015, 03:42
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:30) correct 29% (01:57) wrong based on 226 sessions

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In the xy-coordinate system, the distance between points $$(2\sqrt{3}, \ -\sqrt{2})$$ and $$(5\sqrt{3}, \ 3\sqrt{2})$$ is approximately

A. 4.1
B. 5.9
C. 6.4
D. 7.7
E. 8.1

Kudos for a correct solution.

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Re: In the xy-coordinate system, the distance between points  [#permalink]

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26 Mar 2015, 06:27
1
D

distance =sqrt(x2-x1)2 +(y2-y1)2 (2 outside brackets stands for sqaure)

distance=sqrt32+27
=sqrt59

approx 7.7
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Re: In the xy-coordinate system, the distance between points  [#permalink]

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26 Mar 2015, 10:32
1
The distance is
$$\sqrt{(5\sqrt{3}-2\sqrt{3})^2+(3\sqrt{2}+\sqrt{2})^2}=\sqrt{(3\sqrt{3})^2+(4\sqrt{2})^2}=\sqrt{9\cdot 3+16\cdot 2}=\sqrt{59}$$
since $$7^2=49$$ and $$8^2=64$$, $$7<\sqrt{59}<8$$. Only D. gives a possible value and is the correct answer
Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: In the xy-coordinate system, the distance between points  [#permalink]

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30 Mar 2015, 02:43
Bunuel wrote:
In the xy-coordinate system, the distance between points $$(2\sqrt{3}, \ -\sqrt{2})$$ and $$(5\sqrt{3}, \ 3\sqrt{2})$$ is approximately

A. 4.1
B. 5.9
C. 6.4
D. 7.7
E. 8.1

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

distancebetweenpoints_text.PNG [ 19.29 KiB | Viewed 3752 times ]

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Re: In the xy-coordinate system, the distance between points  [#permalink]

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31 Mar 2015, 11:33
Bunuel wrote:
In the xy-coordinate system, the distance between points $$(2\sqrt{3}, \ -\sqrt{2})$$ and $$(5\sqrt{3}, \ 3\sqrt{2})$$ is approximately

A. 4.1
B. 5.9
C. 6.4
D. 7.7
E. 8.1

Kudos for a correct solution.

Distance = sqrt[(3sqrt(2) + sqrt(2))^2+ (5sqrt(3) - 2sqrt(3))^2
= sqrt[4sqrt(2) + 3 sqrt(3)]
= sqrt(59)
Now, 7^2 = 49 and 8^2 = 64
So, answer lies between 7 and 8,
Hence option (D).

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Re: In the xy-coordinate system, the distance between points  [#permalink]

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28 Dec 2017, 21:36
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).

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Re: In the xy-coordinate system, the distance between points &nbs [#permalink] 28 Dec 2017, 21:36
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