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
1) 20
2) 50
3) 100
4) 200
5) 400
Determine the y-intercepts by plugging in x=0: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
|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.
