# 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))
```