region on the coordinate plane

nahid078 wrote:If 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

Determine the y-intercepts by plugging in x=0:
|0/2| + |y/2| = 5
|y/2| = 5
y = ±10.
Thus, the y-intercepts are (0, 10) and (0, -10).

Determine the x-intercepts by plugging in y=0:
|x/2| + |0/2| = 5
|x/2| = 5
x = ±10.
Thus, the x-intercepts are (-10, 0) and (10, 0).

Link together (-10, 0), (0, 10), (10, 0) and (0, -10).
The following graph is yielded:


The resulting graph is a square with a diagonal of length 20.
For any square with side s, the length of the diagonal = s√2.
Since s√2 = 20, we get:
s = 20/√2
A = s² = (20/√2)² = 400/2 = 200.

The correct answer is D.

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If 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

when y=0, |x/2|=5, |x|=10, x=-10,10 and when x=0 |y/2|=5, |y|=10, y=-10,10. Therefore there are 4 points (-10,-10),(-10,10),(10,-10),(10,10) and we have parallelogram. The area is =(1/2)20*20=200, therefore the answer is D.


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