Find the area of the plane area displayed by the inequality group

Let's draw the figure first, discuss first, 1) If x>=0, y>=0

then x 2+y 2<=|x|+|y|It is simplified to x2+y 2<=x+y

That is, (x-1 2) 2+(y-1 2) 2<=1 2

2) If x<0, y>=0

then x 2+y 2<=|x|+|y|It is simplified to x2+y 2<=x+y

That is, (x-1 2) 2+(y-1 2) 2<=1 2

3) If x<0 and y<0 then the graph at this time is (x+1 2) 2+(y+1 2) 2<=1 2

4) If x>=0 and y<0, then the graph is (x-1 2) 2+(y+1 2) 2<=1 2

So we get the graph as:

x-1 2) 2+(y-1 2) 2<=1 2 (when (x,y) is in the first quadrant).

x+1 2) 2+(y-1 2) 2<=1 2 (when (x,y) is in the second quadrant).

x+1 2) 2+(y+1 2) 2<=1 2 (when (x,y) is in the third quadrant).

x-1 2) 2+(y+1 2) 2<=1 2 (when (x,y) is in the fourth quadrant).

Then these points have to meet the condition y x, just draw a picture.

And then the area will be asked?

You've drawn all the pictures, still can't you? The plane area of y x is above y=x, and if you draw it inaccurately, the radius of the circle should be (1 2), which is greater than 1 2, so your graph is not accurate.

Vulture 2+1

Minute x>0, y>0; x>0,y<0;x<0,y>0;x<0, y<0 to discuss the first formula, simplified should be four quadrants, each quadrant has a semicircle, and then consider the second formula.

Slightly inequality x y 6 0 represents the set of points on the line x y 6 = 0 and the lower right, x y 0 represents the set of points on the line x y = 0 and the upper right of the line, x 3 represents the set of points on the line x = 3 and to the left, so the plane area represented by the inequality group is shown in the figure, so the area of the region is also the area of abc, obviously abc is an isosceles right triangle, silver a=90°, ab=ac, b(3, Jane Chi Shu 3), from the point to the straight line distance of the male blocker:

First, draw the plane area represented by the inequality group, and then find it by the triangle area formula, that is, roll only the <> of the mountain travel

b(3,-3) is obtained

by <>

c(3,8) is obtained

by <>

A(-<

s △abc =<>

bc•d=<>

<> so the answer is: <>

x 2,y 0,y x-1 represents a triangle with (1,0), (2,0), and (2,1) as vertices.

The area is the donor, I see that your bones are strange, the Qiyu Xuan is high, and there are wisdom roots, you are a martial arts wizard in ten thousand.

Concentrate on practice, and the key state will become a big weapon, and there is a small test for the contemptible people, please click on the other questions next to the answer, please ask another question, thank you.

The plane area represented by the group of inequalities: x 0, y 0, x + y 2 is a triangle surrounded by three points (0,0), (0,2), (2,0), this triangle is an isosceles right triangle, and the length of the waist is equal to 2.

Area of the planar area = 1 2 * bottom * height = 1 2 * 2 * 2 = 2

Unequal stupid posture group: x 0, with Qi book containing y 0, x+y 2 represents the plane area is a triangle surrounded by three points (0,0), (0,2), (2,0), this triangle is an isosceles right triangle, and the length of the two right angles is equal to 2, so.

Area of the planar area = 1 2 * bottom * height = 1 2 * 2 * 2 = 2

Draw four straight lines, the black diagonal part is the area to be found, and subtract the area of the two triangles from the trapezoidal area.

<> the light is a little dim, sorry.

y≥|x+1|-1

x>=-1 y>=x

x<=-1 y>=-x-2

y≤-|x|+1

x>=0 y<=-x-1

x<=0 y<=x+1

The area drawn in the coordinate system is a rectangle. The width is 2 2 for the root number, the length is 3 * the root number 2 2 2 for the area is 3 2

First draw the plane area represented by the inequality group, and then find it by the triangle area formula [Exciting brother analysis] Make the equality group to represent the flat lead surface area, as shown in the figure abc from , can get b(3,-3) from , can get c(3,8) from , can get a(- good front s abc = bc d= 11 (3+) so the answer is: