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Goemetry Q

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Goemetry Q

by dev.gavande » Tue Oct 04, 2011 12:05 am
If equation encloses a certain region on the coordinate plane, what is the area of this region?
"¢ 20
"¢ 50
"¢ 100
"¢ 200
"¢ 400

My answer is 100, its wrong. Need to know why.
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by sl750 » Tue Oct 04, 2011 12:06 am
Is this question in its entirety?
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by Anurag@Gurome » Tue Oct 04, 2011 12:06 am
dev.gavande wrote:If equation encloses a certain region on the coordinate plane, what is the area of this region?
"¢ 20
"¢ 50
"¢ 100
"¢ 200
"¢ 400

My answer is 100, its wrong. Need to know why.
What is the equation?
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by dev.gavande » Tue Oct 04, 2011 12:11 am
Sorry did'nt see preview. here is the equation
If equation |x/2|+|y/2|=5 encloses a certain region on the coordinate plane, what is the area of this region?
"¢ 20
"¢ 50
"¢ 100
"¢ 200
"¢ 400
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by Anurag@Gurome » Tue Oct 04, 2011 12:16 am
dev.gavande wrote:Sorry did'nt see preview. here is the equation
If equation |x/2|+|y/2|=5 encloses a certain region on the coordinate plane, what is the area of this region?
"¢ 20
"¢ 50
"¢ 100
"¢ 200
"¢ 400
|x/2| + |y/2| = 5 implies |x| + |y| = 10

If you split this into the 4 possible values:

x + y = 10, x - y = 10, -x - y = 10, -x + y = 10
The above equations are lines with slopes -1, 1, -1, and 1 respectively.

If we graph this, it will be a rhombus with center at the origin.
Total Area = 1/2 (20 * 20) = 200

The correct answer is D.
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by dev.gavande » Tue Oct 04, 2011 12:53 am
I am sorry i am not getting this... till the slopes its fine.
how did you figure it will be a rhombus?
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by GmatKiss » Tue Oct 04, 2011 5:49 am
Same doubt here! and how is it 1/2 (20 * 20)?!
Waiting for clarifications.

TIA,
GK
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by shankar.ashwin » Tue Oct 04, 2011 11:26 am
You get these 4 equations removing the modulus

x + y = 10, x - y = 10, -x - y = 10, -x + y = 10

Plot the lines in a graph, You get (0,10) (0.-10) (10,0) (-10,0) - A diamond shaped figure with center at origin. (Sub x=0 or y=0 in all the equations and plot the extreme values)

The 2 diagonals are 20 units and all 4 sides are equal, You could find the area of the rhombus.
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