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# Points X, Y, and Z are located on the rectangular coordinate

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Points X, Y, and Z are located on the rectangular coordinate [#permalink]  14 Feb 2012, 05:04
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Points X, Y, and Z are located on the rectangular coordinate plane at points (2; 3), (-4; 3), and (2; -3), respectively. What is the length of line segment YZ?

A. 6
B. 6*root(2)
C. 7
D. 8
E. 9

[Reveal] Spoiler:
The OA = B 6*root(2)

My Q is why cant we use the distance formula for Y / Z and get the length = 6
[Reveal] Spoiler: OA

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Last edited by Bunuel on 14 Feb 2012, 05:39, edited 1 time in total.
Edited the question
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Re: Length of segment [#permalink]  14 Feb 2012, 05:22
Well of course you can use the distance formula but do realize that the distance formula is not really covered by the Original Guide. Hence, they had to provide a 3rd coordinate to make it a right angled triangle so that you could use the pythagorus theorem. Using the distance formula:

For 2 points: A & B, Distance between A and B $$=\sqrt{({(x_1-x_2)}^2 + {(y_1-y_2)}^2)}$$
Where $$A=(x_1,y_1)$$ & $$B=(x_2,y_2)$$

In the question above $$Y=(-4,3)$$ & $$Z=(2,-3)$$
Distance between 2 points, Y & Z, on the coordinate system $$=\sqrt{({(-4-2)}^2 + {(3+3)}^2)}$$

Which is $$=\sqrt{(6^2 + 6^2)}$$
Which is $$=\sqrt{72}$$
Which is $$=6\sqrt{2}$$

So Yes, to answer your question, info about $$Y$$ & $$Z$$ alone is sufficient "if you know the formula for deriving the distance between two coordinates", but otherwise you need to know a third point to first establish it is a right angled triangle. Works either ways. I have seen numerous statistics questions where GMAT actually gives you the formula for calculating the sum of the series, even though we need to know it to solve quite a few question on the GMAT. Either ways, your pick. Answer still remains the same $$=6\sqrt{2}$$ and not $$6$$!
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Re: Points X, Y, and Z are located on the rectangular coordinate [#permalink]  14 Feb 2012, 05:58
Expert's post
rxs0005 wrote:
Points X, Y, and Z are located on the rectangular coordinate plane at points (2; 3), (-4; 3), and (2; -3), respectively. What is the length of line segment YZ?

A. 6
B. 6*root(2)
C. 7
D. 8
E. 9

[Reveal] Spoiler:
The OA = B 6*root(2)

My Q is why cant we use the distance formula for Y / Z and get the length = 6

You can use the distance formula to calculate the length of line segment YZ

The formula to calculate the distance between two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ is $$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$.

Thus $$YZ=\sqrt{(-4-2)^2+(3-(-3))^2}=6\sqrt{2}$$.

Answer: B.

If you are not aware of this formula then you can easily get the answer by drawing the triangle:
Attachment:

xy-plane.PNG [ 15.5 KiB | Viewed 2276 times ]
As you can see XYZ is not only the right triangle but isosceles right triangle (YX=YZ=6), so it's 45-45-90 right triangle were the sides are always in the ratio $$1:1:\sqrt{2}$$, thus $$YZ=6\sqrt{2}$$. Else you can use Pythagorean theorem to get YZ.

Answer: B.

For more on Coordinate Geometry check: math-coordinate-geometry-87652.html

Hope it helps.
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Re: Points X, Y, and Z are located on the rectangular coordinate [#permalink]  27 Jun 2013, 22:46
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

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Re: Points X, Y, and Z are located on the rectangular coordinate [#permalink]  28 Jun 2013, 03:15
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Expert's post
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Consider the Points X (2, 3) and Y (-4, 3). Since Y value of both the points is same(3) so the line must be parallel to X axis and the distance between X and Y must be |2| + |-4| = 6

Similarly in Points X (2, 3) and Z (2, -3), X value of both the points is same(2) so the line must be parallel to Y axis and the distance between X and Z must be |3| + |-3| = 6

We have a 45-45-90 triangle with XY, XZ sides and YZ Hypotenuses.

Since sides of any 45-45-90 triangle are always in ratio 1 : 1 : $$\sqrt{2}$$ ------> XY : XZ : YZ must be 6 : 6 : 6$$\sqrt{2}$$

Hence YZ = 6$$\sqrt{2}$$ Choice B
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Re: Points X, Y, and Z are located on the rectangular coordinate   [#permalink] 28 Jun 2013, 03:15
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# Points X, Y, and Z are located on the rectangular coordinate

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