SICP - Solution: Exercise 2.2

January 5, 2019

Exercise 2.2 #

Consider the problem of representing line segments in a plane. Each segment is represented as a pair of points: a starting point and an ending point. Define a constructor make-segment and selectors start-segment and end-segment that define the representation of segments in terms of points. Furthermore, a point can be represented as a pair of numbers: the $x$ coordinate and the $y$ coordinate. Accordingly, specify a constructor make-point and selectors x-point and y-point that define this representation. Finally, using your selectors and constructors, define a procedure midpoint-segment that takes a line segment as argument and returns its midpoint (the point whose coordinates are the average of the coordinates of the endpoints). To try your procedures, you’ll need a way to print points:

(define (print-point p)
  (newline)
  (display "(")
  (display (x-point p))
  (display ",")
  (display (y-point p))
  (display ")"))

Solution #

; --- Points ---
(define (make-point x y) (cons x y))
(define (x-point p) (car p))
(define (y-point p) (cdr p))

(define (print-point p)
  (newline)
  (display "(")
  (display (x-point p))
  (display ",")
  (display (y-point p))
  (display ")"))

; --- Segments ---
(define (make-segment p1 p2) (cons p1 p2))
(define (start-segment s) (car s))
(define (end-segment s) (cdr s))

(define (print-segment s)
  (newline)
  (display "[")
  (print-point (start-segment s))
  (display ",")
  (print-point (end-segment s))
  (display "]"))

(define (midpoint-segment s)
  (make-point (/ (+ (x-point (start-segment s)) (x-point (end-segment s))) 2)
              (/ (+ (y-point (start-segment s)) (y-point (end-segment s))) 2)))

; --- Test ---

(print-point (make-point 2 3))

(define p1 (make-point 2 3))
(define p2 (make-point 5 6))
(define s1 (make-segment p1 p2))
(print-segment s1)
(print-point (midpoint-segment s1))