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02 Apr 2020, 10:26
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C
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Difficulty:
45%
(medium)
Question Stats:
60% (01:05) correct
40%
(01:32)
wrong
based on 258
sessions
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The area of the closed region bounded by the equation |x| + |y| = 2 in the two-dimensional plane is
A. 4
B. 2π
C. 8
D. 10
E. 4π
A. 4
B. 2π
C. 8
D. 10
E. 4π
02 Apr 2020, 15:47
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The closed region bounded by the equation |x| + |y| = 2 is a square, whose diagonal is 4 units long.
Area = \(\frac{(diagonal)^2}{2} = \frac{4^2}{2} = 8\)
Area = \(\frac{(diagonal)^2}{2} = \frac{4^2}{2} = 8\)
Bunuel
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General Discussion
15 Dec 2021, 03:48
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|x|+|y| = 2
|y| = -|x|+2
a) x>0 & y>0
y = -x+2 (Equation of line)
x-intercept = 2
b) x>0 & y<0
-y = -x+2
y = x-2 (Equation of line)
x-intercept = 2
c) x<0 & y>0
y = -(-x)+2
y = x+2 (Equation of line)
x-intercept = -2
d) x<0 & y<0
-y = -(-x)+2
y = -x-2 (Equation of line)
x-intercept = -2
All these 4 lines when drawn on graph will form a Rhombus where length of each diagonal = 4 units (|2-(-2)|)
Area of Rhombus = Product of diagonals/2 = 4*4/2 = 8 units (C)
|y| = -|x|+2
a) x>0 & y>0
y = -x+2 (Equation of line)
x-intercept = 2
b) x>0 & y<0
-y = -x+2
y = x-2 (Equation of line)
x-intercept = 2
c) x<0 & y>0
y = -(-x)+2
y = x+2 (Equation of line)
x-intercept = -2
d) x<0 & y<0
-y = -(-x)+2
y = -x-2 (Equation of line)
x-intercept = -2
All these 4 lines when drawn on graph will form a Rhombus where length of each diagonal = 4 units (|2-(-2)|)
Area of Rhombus = Product of diagonals/2 = 4*4/2 = 8 units (C)
