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#lang racket
(define/contract (is-boomerang points)
(-> (listof (listof exact-integer?)) boolean?)
(match points
[(list-no-order a b c) #:when (equal? a b) #false] ; Are any two points the same?
[(list (list x _) (list x _) (list x _)) #false] ; Are they on a horizontal line?
[(list (list _ y) (list _ y) (list _ y)) #false] ; Are they on a vertical line?
[(list-no-order (list x1 _) (list x2 _) (list x3 _)) ; Are two points on a horizontal line,
#:when (and (= x1 x2) ; but the third point isn't?
(not (= x1 x3))) #true]
[(list-no-order (list _ y1) (list _ y2) (list _ y3)) ; Are two points on a vertical line,
#:when (and (= y1 y2) ; but the third point isn't?
(not (= y1 y3))) #true]
[(list (list x1 y1) (list x2 y2) (list x3 y3)) ; If none of the special cases apply,
(let ([m (/ (- y2 y1) (- x2 x1))]) ; calculate the slope between two points
(not (= y3 (+ y1 (* m (- x3 x1))))))])) ; and see if the line passes through the third
(is-boomerang '((1 1) (2 3) (3 2)))
(is-boomerang '((1 1) (2 2) (3 3)))
(is-boomerang '((0 0) (0 2) (2 1)))
(is-boomerang '((0 0) (1 1) (1 1)))
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