Absolute Area

bigmonkey31 wrote:'If equation |x/2| + |y/2| = 5 encloses a region on the coordinate plane, what is the area of this region?

a) 20
b) 50
c) 100
d) 200
e) 400

OA D

I'm a bit confused by the OE... anyone have a good coherent answer? I appreciate it!

|x/2| + |y/2| = 5 gives for equations

x+y =10
x-y =10
x+y = -10
and x-y =-10

Refer the pic

The area enclosed = area of 2 triangles with base 20 and height 10 = 2*1/2*20*10 = 200

bigmonkey31 wrote:'If equation |x/2| + |y/2| = 5 encloses a region on the coordinate plane, what is the area of this region?

a) 20
b) 50
c) 100
d) 200
e) 400

OA D

I'm a bit confused by the OE... anyone have a good coherent answer? I appreciate it!

As we have the modulus sign,we know that 4 lines have to be taken into account.
Thus,we have a rhombus(As all four sides are equal)
By symmetry,we know that Total Area = 4 x Area in a single quadrant.
Noe,considering x/2 + y/2 =5
Put x=0,y = 10
Put y=0,x=10
Thus,we have the pts. of intersection.
Area of Triangle = 1/2 x base x altitude = 1/2 x 10 x 10 = 50

Hence,[spoiler]total area = 4 x 50 = 200 which is D.
[/spoiler]
Hope,you understand the problem approach.Still,if you have got any query you can submit in the successive posts.

just put x=0 then y=+/- 10
and when y=0 ; x=+/-10

wit ths 4 value if u draw on coordinates u get a rhombus with diagonals 20 each

area of rhombus=1/2 d1*d2=1/2*(20*20)=200

bigmonkey31 wrote:'If equation |x/2| + |y/2| = 5 encloses a region on the coordinate plane, what is the area of this region?

a) 20
b) 50
c) 100
d) 200
e) 400

OA D

I'm a bit confused by the OE... anyone have a good coherent answer? I appreciate it!

|x/2| + |y/2| = 5 --> |x| + |y| = 10 This is the equation of a rhombus which cuts x and y axis at (10,0),(-10,0) and (0,10),(0,-10) respectively.
so area of rhombus = 1/2* 20 * 20 = 200
Ans D

bigmonkey31 wrote:'If equation |x/2| + |y/2| = 5 encloses a region on the coordinate plane, what is the area of this region?

a) 20
b) 50
c) 100
d) 200
e) 400

OA D

I'm a bit confused by the OE... anyone have a good coherent answer? I appreciate it!

|x|+|y|=k will always yield an square with center at origin and (k,0),(0,k),(-k,0) and (0,-k) as the vertices of the square. Area of this square= 2*k^2

Now using your example |x/2| + |y/2| = 5 can be written as |x|+|y|=10
Thus area=2*10^2=200 sq. units.

hence D