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 ")"))
This program takes most of it’s design from the rational number example.
(define (make-segment p1 p2)
(cons p1 p2))
(define (start-segment s)
(car s))
(define (end-segment s)
(cdr s))
(define (average a b) (/ (+ a b) 2.0))
(define (make-point x y)
(cons x y))
(define (x-point p)
(car p))
(define (y-point p)
(cdr p))
(define (midpoint-segment s)
(make-point
(average
(x-point (start-segment s))
(x-point (end-segment s)))
(average
(y-point (start-segment s))
(y-point (end-segment s)))
))
(define (print-point p)
(newline)
(display "(")
(display (x-point p))
(display ",")
(display (y-point p))
(display ")"))
> (print-point (midpoint-segment
(make-segment
(make-point 1 1)
(make-point 8 4))))
(4.5,2.5)
> (print-point (midpoint-segment
(make-segment
(make-point 0 0)
(make-point 4 4))))
(2.,2.)
> (print-point (midpoint-segment
(make-segment
(make-point -1 -4)
(make-point 1 4))))
(0,0)