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# 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)