1 (define (make-point x y)
2   (cons x y))
3 (define (x-point p)
4   (car p))
5 (define (y-point p)
6   (cdr p))
7 
8 (define (make-segment start end)
9   (cons start end))
10 (define (start-segment seg)
11   (car seg))
12 (define (end-segment seg)
13   (cdr seg))
14 (define (midpoint-segment seg)
15   (define (average x y)
16     (/ (+ x y) 2))
17   (let ((x1 (x-point (start-segment seg)))
18 	(x2 (x-point (end-segment seg)))
19 	(y1 (y-point (start-segment seg)))
20 	(y2 (y-point (end-segment seg))))
21     (make-point (average x1 x2)
22 		(average y1 y2))))
23 
24 (define (print-point p)
25   (newline)
26   (display "(")
27   (display (x-point p))
28   (display ",")
29   (display (y-point p))
30   (display ")"))
31 
32 (define x1y2 (make-point 1 2))
33 (define x-4y-3 (make-point -4 -3))
34 (define x1y2tox-4y-3 (make-segment x1y2 x-4y-3))
35 (print-point (midpoint-segment x1y2tox-4y-3))
36 (display "=(-3/2,-1/2)")
37 
38 ;; Exercise 2.3.  Implement a representation for rectangles in a plane. (Hint: You may want to make use of exercise 2.2.) In terms of your constructors and selectors, create procedures that compute the perimeter and the area of a given rectangle. Now implement a different representation for rectangles. Can you design your system with suitable abstraction barriers, so that the same perimeter and area procedures will work using either representation? 
39 
40 ;; makes rectangle given 2 points: top-left and bottom-right
41 (define (make-rect tl br)
42   (let ((tr (make-point (x-point br) (y-point tl)))
43 	(bl (make-point (x-point tl) (y-point br))))
44     (cons (cons tl tr)
45 	  (cons bl br))))
46 (define (top-left rect)
47   (caar rect))
48 (define (bot-right rect)
49   (cddr rect))
50 (define (top-right rect)
51   (cdar rect))
52 (define (bot-left rect)
53   (cadr rect))
54 
55 (define (width rect)
56   (- (x-point (top-right rect)) (x-point (top-left rect))))
57 (define (height rect)
58   (- (y-point (top-left rect)) (y-point (bot-left rect))))
59 
60 (define (perimeter rect)
61   (+ (* 2 (width rect))
62      (* 2 (height rect))))
63 (define (area rect)
64   (* (width rect) (height rect)))
65 
66 (define (test-case actual expected)
67   (load-option 'format)
68   (newline)
69   (format #t "Actual: ~A Expected: ~A" actual expected))
70 
71 (define tl (make-point 1 6))
72 (define br (make-point 10 3))
73 (define rect (make-rect tl br))
74 (test-case (perimeter rect) 24)
75 (test-case (area rect) 27)
76 
77 ;; makes rectangle given top-left corner, width, and height
78 (define (make-rect top-left width height)
79   (cons top-left (cons width height)))
80 (define (top-left rect)
81   (car rect))
82 (define (bot-right rect)
83   (make-rect (+ (x-point (top-left rect))
84 		(width rect))
85 	     (- (y-point (top-left rect))
86 		(height rect))))
87 (define (top-right rect)
88   (make-rect (+ (x-point (top-left rect))
89 		(width rect))
90 	     (y-point (top-left rect))))
91 (define (bot-left rect)
92   (make-rect (x-point (top-left rect))
93 	     (- (y-point (top-left rect))
94 		(height rect))))
95 
96 (define (width rect)
97   (cadr rect))
98 (define (height rect)
99   (cddr rect))
100 
101 (define rect (make-rect tl 9 3))
102 (test-case (perimeter rect) 24)
103 (test-case (area rect) 27)