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Equation |x/2|+|y/2|=5 encloses a certain region on the

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Manager
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Equation |x/2|+|y/2|=5 encloses a certain region on the [#permalink] New post 03 Apr 2007, 14:06
Equation |x/2|+|y/2|=5 encloses a certain region on the coordinate plane. what is the are of this region?

20
50
100
200
400

Can someone please explain
Manager
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 [#permalink] New post 03 Apr 2007, 14:27
100 for me... It's a long wild shot.
we can get
|x| + |y| = 10

this will be true if the co-ordinates of the enclosed area are
5,5
5,-5
-5,-5 &
-5,5

distance works out to 10
and 10*10 = 100

However the co-ordinates could just as easily be
6,4 or
7,-3 etc.,

haven't checked these possibilities. I think this should be sufficient ...but again I haven't checked... the shapes coming out are too weird for me to calculate their areas.
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 [#permalink] New post 03 Apr 2007, 14:54
Should be D.
In Ist quad x+y = 10 => x intersect (0,10), y intersect (10,0) +> area of triangle => 1/2*10*10 => 50

Similarly calculate of triangles in other quadrants.

Total area = 50+50+50+50 => 200.
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 [#permalink] New post 03 Apr 2007, 14:59
Just found a superb answer
http://www.gmatclub.com/phpbb/viewtopic ... =challenge

thanks for your help guys
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 [#permalink] New post 03 Apr 2007, 18:18
my approach is -

Line x/a + y/b = 1 where a and b are intercepts on x and y axis respectively.
given line |x|/10 + |y|/10 = 1

Exploring all possible values the area of the triangle = 4 * (1/2 *10 *10) =200
Answer is 'D'
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Re: Coordinate Geometry [#permalink] New post 03 Apr 2007, 22:58
fmeinsen wrote:
Equation |x/2|+|y/2|=5 encloses a certain region on the coordinate plane. what is the are of this region?

20
50
100
200
400

Can someone please explain



I liked the question. probably the question meant the maximum area.

since |x/2|+|y/2| = 5
|x|+|y| = 10

we donot know the values of x and y. they could be +ve or -Ve. if so, x can be a minimum of -10 and a maximum of 10 and do does y. therefore,

x = -10 or 10
y = -10 or 10

if we draw a pricture, it becomes a square with a side of 10-(-10) = 20.
then the area = 20 x 20 = 400.
Re: Coordinate Geometry   [#permalink] 03 Apr 2007, 22:58
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