Turkish wrote:
What is the area of four sided figure formed by the intersection of the set of lines represented by |2x|+|y| = 6?
1. 18
2.24
3.30
4.36
5.48
we just need four XY pair to define the four-sided figure.
Lets works with the concept of X and Y intercepts
When |x|=0; then |y|=6 .. right
y=-6 and 6 ; XY pairs are {0,-6} and {0,6}
when |y|=0 then |2x|= 6
x=-3 and 3 ; The XY pairs are (-3,0 and 3,0)
When you plot these XY pairs you will see that you get a diamond shaped figure (an upright RHOMBUS ) which can be divided into 2 equal triangles. the base of these two triangles is the x-axis
Now area of a triangle = 1/2 * base * height = 1/2 * 6*6 (the distance between -3 and 3 is 6) and the height is 6-0 = 6
Therefore Area of the triangle = \(\frac{1}{2}*36\) =====>18
There are 2 such triangle
Total area = 2*18 =36
ANSWER IS D
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