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Equation |x/2| +|y/2|=5 encloses a certain region on the [#permalink ]
09 Sep 2007, 14:26

Equation |x/2| +|y/2|=5 encloses a certain region on the coordinate plane..
What is the area of the region?
A 20
B. 50
C. 100
D. 200
E. 400
I read the explanation
I have no idea how we know the above region encloses a square
I am totally lost on this
Can anyone help me out?

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Re: Geometry Question-Not sure where they got the theory [#permalink ]
09 Sep 2007, 14:44

jamesrwrightiii wrote:

Equation |x/2| +|y/2|=5 encloses a certain region on the coordinate plane. What is the area of the region? A 20 B. 50 C. 100 D. 200 E. 400 I read the explanation I have no idea how we know the above region encloses a square I am totally lost on this Can anyone help me out?

draw xy plane. go for 10 left, right, up and down. then you get a square with a side of 10sqrt2.

so the ares = (10sqrt^2)^2 = 200

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I am still confused though...actually the answer is C
I am still confused how you know it's a square..
If you multiply everything by 2, then you have X + Y=10
Why can't you have numbers such as 6 and 4..or 8 and 2..or 9 and 1?

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jamesrwrightiii wrote:

I am still confused though...actually the answer is C I am still confused how you know it's a square.. If you multiply everything by 2, then you have X + Y=10 Why can't you have numbers such as 6 and 4..or 8 and 2..or 9 and 1?

no fistail is right... it is 200 (choice D)

just draw it into a plan and you notice that it is a square with side of 10*sqrt(2)

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Re: Geometry Question-Not sure where they got the theory [#permalink ]
09 Sep 2007, 15:17

Fistail wrote:

jamesrwrightiii wrote:

Equation |x/2| +|y/2|=5 encloses a certain region on the coordinate plane. What is the area of the region? A 20 B. 50 C. 100 D. 200 E. 400 I read the explanation I have no idea how we know the above region encloses a square I am totally lost on this Can anyone help me out?

draw xy plane. go for 10 left, right, up and down. then you get a square with a side of 10sqrt2.

so the ares = (10sqrt^2)^2 = 200

Ok here is what I am confused about..

All the equation says is that |x|+|y|=10

I am just not sure how we know to go 10 over for each side when all the equation says is that X and Y need to equal 10...?

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Re: Geometry Question-Not sure where they got the theory [#permalink ]
09 Sep 2007, 15:38

well to be more specific..its the x^2-y^2 plane

if x^2=0 then y^2=-10

if x^2=10 then y^2=0

now remember this |x| and |y| so -y^2=10 when -x^2=0 etc..

you will realize that the region is a square..and that the side of the square is sqrt(2)10.

area of the square=200

Fistail wrote:

jamesrwrightiii wrote:

Equation |x/2| +|y/2|=5 encloses a certain region on the coordinate plane. What is the area of the region? A 20 B. 50 C. 100 D. 200 E. 400 I read the explanation I have no idea how we know the above region encloses a square I am totally lost on this Can anyone help me out?

draw xy plane. go for 10 left, right, up and down. then you get a square with a side of 10sqrt2.

so the ares = (10sqrt^2)^2 = 200

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Re: Geometry Question-Not sure where they got the theory [#permalink ]
02 Jun 2008, 18:49

If I consider the following points (-5,5), (5,5), (-5,-5) and (5,-5), the figure enclosed is a square with an area of 100 sq units. Should the question be what is the max area of the region? Thanks.

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Re: Geometry Question-Not sure where they got the theory [#permalink ]
03 Jun 2008, 02:45

I agree with rakesh22.It should be a square of each side 10. so area is 100 i.e. C

rakesh22 wrote:

If I consider the following points (-5,5), (5,5), (-5,-5) and (5,-5), the figure enclosed is a square with an area of 100 sq units. Should the question be what is the max area of the region? Thanks.

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Re: Geometry Question-Not sure where they got the theory [#permalink ]
03 Jun 2008, 06:34

you know what i agree with 100..cause we only focus on half of the square... walker..what do u think?

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Re: Geometry Question-Not sure where they got the theory [#permalink ]
03 Jun 2008, 06:40

Look at the first quadrant (x >0, y > 0) : x + y = 10, so we get a line segment with endpoints (0,10) and (10,0). We will get a square that can be broken up into 4 right triangles, each with area (10)(10)/2 = 50

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Re: Geometry Question-Not sure where they got the theory [#permalink ]
03 Jun 2008, 06:42

kevincan wrote:

Look at the first quadrant (x >0, y > 0) : x + y = 10, so we get a line segment with endpoints (0,10) and (10,0). We will get a square that can be broken up into 4 right triangles, each with area (10)(10)/2 = 50

but arent we only looking for the triangles in region 1 and 2?

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Re: Geometry Question-Not sure where they got the theory [#permalink ]
03 Jun 2008, 06:49

never mind.. i got confused by the other posters..grrrrrrr this is 200.. |x|+|y|=10 condition1 x>0 y>0 x+y=10...you get a triangle with slope 10sqrt(2) condition 2 x<0 y<0 -x-y=10 -y=10+x.. condition 3 x>0 y<0 x-y=10 -y=10-x and condition 4 x<0 y>0 -x+y=10 y=10+x

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Re: Geometry Question-Not sure where they got the theory [#permalink ]
03 Jun 2008, 07:07

fresinha12 wrote:

never mind.. i got confused by the other posters..grrrrrrr this is 200.. |x|+|y|=10 condition1 x>0 y>0 x+y=10...you get a triangle with slope 10sqrt(2) condition 2 x<0 y<0 -x-y=10 -y=10+x.. condition 3 x>0 y<0 x-y=10 -y=10-x and condition 4 x<0 y>0 -x+y=10 y=10+x

I really dont see how ur getting sides of 10sqrt2.

You plug in for x or y in the original and you get 5,-5,5,-5 etc...

This is square w/ sides of 10.

What am I missing here?

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Re: Geometry Question-Not sure where they got the theory [#permalink ]
03 Jun 2008, 07:12

GMATBLACKBELT wrote:

fresinha12 wrote:

I really dont see how ur getting sides of 10sqrt2.

You plug in for x or y in the original and you get 5,-5,5,-5 etc...

This is square w/ sides of 10.

What am I missing here?

ok lets see..

|x/2|+|y/2|=5

=> |x|+|y|=10

suppose x=0 and y is positive..y/2=5 y=10..

get it? the question is asking about the area occupied by the region given by the equation |x|+|y|=10..

the |x/2|+|y/2| is just to throw you off..the actual equation is |x|+|y|=10

Re: Geometry Question-Not sure where they got the theory
[#permalink ]
03 Jun 2008, 07:12