Stuff

> restart;with(plots):with(geometry):
Warning, the name changecoords has been redefined


First define the points  using the point command in the geometry  package. 

> point(pointA,7,23); point(pointB,20,20); point(pointC,25,23); point(pointD,2,20);

                                pointA


                                pointB


                                pointC


                                pointD

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Now sketch the points using the draw command in the geometry  package  to see which points define which corners of the parallelogram.

> draw([pointA,pointB,pointC,pointD]);


Now define the lines connecting the points.


> line(lineDA,[pointD,pointA]);line(lineAC,[pointA,pointC]);line(lineCB,[pointC,pointB]);line(lineBD,[pointB,pointD]);
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Now get the equations of each line.

> eqnDA := Equation(lineDA,[x,y]); eqnAC := Equation(lineAC,[x,y]); eqnCB := Equation(lineCB,[x,y]); eqnBD := Equation(lineBD,[x,y]); 


(a) Use set notation to describe R as a type II region.  Assign your solution expressions to ans1 and ans2 according to the following template:

 R={ (x,y) | ans1 <= x <= ans2,  20 <= y <= 23 } 

> eqnDA := isolate(eqnDA,x);eqnCB := isolate(eqnCB,x);
> 
> ans1:= -94/3+5/3*y;  
> ans2:=  -40/3+5/3*y;
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(b) Use set notation to describe R as a type I region.  Assign your solution expressions to ans3, ans4, ans5, ans6, ans7 and ans8 according to the following template:

 R = Region_1   union    Region_2   union Region_3 where

               Region_1 = { (x,y) | ans3 <= y <= ans4 ,  2 <= x <= 7 } 
and
               Region_2 =  { (x,y) | ans5 <= y <= ans6 ,  7  <= x <=  20 }
and
               Region_3 =  { (x,y) | ans7 <= y <= ans8 , 20 <= x <= 25 }  

> eqnDA:=isolate(eqnDA,y); eqnAC:=isolate(eqnAC,y); eqnCB:=isolate(eqnCB,y);
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> ans3:=  20;
> ans4:=  rhs(eqnDA);
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> ans5:=  20;
> ans6:=  rhs(eqnAC);
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> ans7:=  rhs(eqnCB);
> ans8:=  rhs(eqnAC);