In each of the questions below write the function to produce the output according to problem statement. Make sure to include cases in which program must produce an error. Also put data definitions, contract and test cases $($i$.$e$.$ check$-$expect tests$/$examples$)$ in your programs. You need to add documentation comments only if you find them necessary to describe your approach.

$(20$pts$)$ Design and instantiate a structure which has $2$ fields: color $($line color$),$ positions $($positions of a line$).$ color is represented by a string and positions is represented by a list which has only $2$ elements. Each element is a posn structure with $2$ fields: $x(x$ coordinate$)$ and y coordinate$).x$ and $y$ are represented by numbers. $($Do not forget to write down the functions constructors, selectors, and predicates. Solve Question $2,3$ by using that structure$)$

Distance of two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is given by:

distance $(A,B)=\sqrt[\phantom{2}]{(x_1-x_2{)}^2+(y_1-y_2{)}^2}$

$(40$pts$)$ Design and implement a recursive Racket function which consumes a list of structure as its parameter and produces a list of distance. It uses the formula that is given in first page.

$(15$pts$)$ Use proper abstract list processing functions to do following task: consumes a list of structure as its parameter and produces a list of structure whose color is equal to "red".

Contract for abstract functions for list$-$processing:

filter: Boolean