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Area - Co-ordinate plane

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Area - Co-ordinate plane

by lali_mew » Fri Aug 29, 2008 12:01 pm
Equation |x/2| + |y/2| = 5 encloses a certain region on the coordinate plane. What is the area of this region?
1)20
2)50
3)100
4)200
5)400

OA = 200

I'm not sure how to approach this one because every possible combination of x and y is giving me a different area.
Effectively, x + y = +- 10. Should I be backtracking in this case?
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by mals24 » Fri Aug 29, 2008 1:08 pm
|x/2| + |y/2| = 5

|x| + |y| = 10

with this we can come up with the following equations:

(x+y)=10; (x-y)=10
(-x-y)=10; (-x+y)=10

The slopes of the equations are -1, 1, -1, 1

solving the above equations you will get the following points:
(0,10); (10,0); (0,-10); (-10,0).

plot this on the graph and you will get a square with sides sqrt200.

Hence area of the square will be a^2 = 200

check the graph below



Image
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by lali_mew » Fri Aug 29, 2008 3:40 pm
Thanks mals24!
I still am not sure of how you came up with the 4 co-ordinates though.
I understood the 4 equations. [Thanks, cuz that atleast got me started]
Then, did you arrange each equation in the form y = mx + c and then find the X and Y intercept for each equation? Or is there any other way to deduce the coordinates from the corresponding slopes of 1 and -1.
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by mals24 » Sat Aug 30, 2008 1:01 am
yup you can change the equations in y=mx+c form n then find the co-ords for each equation.
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