Exercise 6.1.1: (back)
> (distance-to-0 (make-posn 3 4))
5
=> (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 (* 2 3) (* 2 4)))
10
=> (make-posn (* 2 3) (* 2 4))
=> (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 (- 6 1)))
13
=> (make-posn (12) (* 2 4))
=> (make-posn (12) (5))
=> (sqrt
(+
(sqr (posn-x (make-posn 12 5)))
(sqr (posn-y (make-posn 12 5)))))
=> (sqrt
(+
(sqr (12))
(sqr (5))))
=> (sqrt
(+ (144) (25)))
=> (sqrt 169)
=> 13