ex063.rkt

;; The first three lines of this file were inserted by DrRacket. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-beginner-reader.ss" "lang")((modname ex063) (read-case-sensitive #t) (teachpacks ((lib "image.rkt" "teachpack" "2htdp") (lib "universe.rkt" "teachpack" "2htdp") (lib "batch-io.rkt" "teachpack" "2htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "image.rkt" "teachpack" "2htdp") (lib "universe.rkt" "teachpack" "2htdp") (lib "batch-io.rkt" "teachpack" "2htdp")) #f)))
; computes the distance of ap to the origin
(define (distance-to-0 ap)
  (sqrt
    (+ (sqr (posn-x ap))
       (sqr (posn-y ap)))))

(check-expect (distance-to-0 (make-posn 3 4)) 5)
(check-expect (distance-to-0 (make-posn 8 6)) 10)
(check-expect (distance-to-0 (make-posn 5 12)) 13)


(distance-to-0 (make-posn 3 4))
;(sqrt (+ (sqr (posn-x (make-posn 3 4))) (sqr (posn-y (make-posn 3 4)))))
;(sqrt (+ (sqr 3) (sqr 4)))
;(sqrt (+ 9 16))
;(sqrt 25)
;5

(distance-to-0 (make-posn 6 (* 2 4)))
;(distance-to-0 (make-posn 6 8)
;(sqrt (+ (sqr (posn-x (make-posn 6 8))) (sqr (posn-y (make-posn 6 8)))))
;(sqrt (+ (sqr 6) (sqr 8)))
;(sqrt (+ 36 64))
;(sqrt 100)
;10

(+ (distance-to-0 (make-posn 12 5)) 10)
;(+ (sqrt (+ (sqr (posn-x (make-posn 12 5))) (sqr (posn-y (make-posn 12 5)))))
;   10)
;(+ (sqrt (+ (sqr 12) (sqr 5))) 10)
;(+ (sqrt (+ 144 25)) 10)
;(+ (sqrt 169) 10)
;(+ 13 10)
;23