SICP exercise 2.02

Problem

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 are pairs of numbers, and segments are pairs of points.

(define (make-point x y)
  (cons x y))
 
(define (x-point p)
  (car p))
 
(define (y-point p)
  (cdr p))
 
(define (make-segment p1 p2)
  (cons p1 p2))
 
(define (start-segment p)
  (car p))
 
(define (end-segment p)
  (cdr p))

Here's the midpoint-segment procedure:

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

Tests:

(print-point (make-point 0 0))

Output:

(0,0)

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

Output:

(3,2)

(define p1 (make-point 1 2))
 
(print-point p1)

Output:

(1,2)

(define p2 (make-point 5 2))
 
(print-point p2)

Output:

(5,2)

(define s1 (make-segment p1 p2))
 
(print-point (midpoint-segment s1))

Output:

(3,2)

(define p3 (make-point 0 0))
 
(define p4 (make-point 5 4))
 
(define s2 (make-segment p3 p4))
 
(print-point (midpoint-segment s2))

Output:

(2.5,2)