# Equation of three lines a,b and c in the following graph are x y=0,x-y=0 and y=2( may not be written in an order). match the given equation with lines a,b and c. also, find the area enclosed between these lines.

1
by devanshupatidar

2015-04-06T22:38:31+05:30

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See diagram.  fig 1:

is the first straightline :  x * y = 0 ?
x * y = 0  is same as ,  x = 0 and y = 0.  So it is the x axis and the y  axis.
x - y = 0  is same as  x = y.  the bisector of x and y axes in the 1st quadrant.
y =2 is the horizontal line.

The area enclosed is a right angle triangle :  the colored area
=  1/2 * 2 * 2 = 2.
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see diagram 2:

Is the first line :  x + y = 0 ?  then it is the bisector of - x and +y  axes in the 2nd quadrant.
x - y = 0    and  y = 2 are same like in the above.
The area enclosed by the three lines is colored.  It is an isosceles triangle.
The area enclosed in the 1st quadrant is =  1/2 * 2 * 2 = 2.
Area enclosed in 2nd quadrant = same as in 1st quadrant = 2.

total area enclosed = 4 units.