FIN312 (b) Given the following 5 test cases, print the results from your function using this...

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FIN312 (b) Given the following 5 test cases, print the results from your function using this code: for p, A, B in cases: print(f"Result: {proximity(p, A, B):3}") No. 1. 2. 3. 4. 5. P 1 2 2 3 4 A (-10, 20) (-6, 6) (2, -1, 6) (-3, 8, -1, 8) (2, -4, 1, 0, 6) Tutor-Marked Assignment B (20, -30) (18,-4) (-1, 3, -6) (2,2,0,9) (-2, 4, 7, 4,-2) (5 marks) Question 2 (a) Let A = (a, a,..., an) and B = (b,b,..., b) be two points in the n-dimensional space R". We can think of each point as a tuple of n real numbers. Define the promixity-p metric between A and B using the formula: D(A,B) = la: - b; P where the symbol |x| represents the absolute value of x. The proximity-p metric is a generalized way to measure 'distance between A and B. Example: Suppose A = (1,1) and B = (5,4) in the 2-dimensional plane. When p = 1, we get the distance to travel along the lines of a square grid. In this case, D(A,B) = proximity (1, (1,1), (5,4)) = 7. When p = 2, we get the familiar 'Euclidean distance from Pythagoras Theorem. In this case, D (A,B) = proximity(2, (1,1), (5,4)) = 5. 5 3 2 1 A = (1, 1) D(A, B) 5 B=(5, 4) D(A, B)=7 Task: Implement the function proximity(p, A, B) that takes in an integer p. point A and point B (each represented as a tuple of n real numbers). The function should compute and return the value of D (A,B) using the given formula. (Note: the value of dimension n is implicit in the lengths of A and B so there is no need to pass it in as a separate argument.) (20 marks) FIN312 (b) Given the following 5 test cases, print the results from your function using this code: for p, A, B in cases: print(f"Result: {proximity(p, A, B):3}") No. 1. 2. 3. 4. 5. P 1 2 2 3 4 A (-10, 20) (-6, 6) (2, -1, 6) (-3, 8, -1, 8) (2, -4, 1, 0, 6) Tutor-Marked Assignment B (20, -30) (18,-4) (-1, 3, -6) (2,2,0,9) (-2, 4, 7, 4,-2) (5 marks) Question 2 (a) Let A = (a, a,..., an) and B = (b,b,..., b) be two points in the n-dimensional space R". We can think of each point as a tuple of n real numbers. Define the promixity-p metric between A and B using the formula: D(A,B) = la: - b; P where the symbol |x| represents the absolute value of x. The proximity-p metric is a generalized way to measure 'distance between A and B. Example: Suppose A = (1,1) and B = (5,4) in the 2-dimensional plane. When p = 1, we get the distance to travel along the lines of a square grid. In this case, D(A,B) = proximity (1, (1,1), (5,4)) = 7. When p = 2, we get the familiar 'Euclidean distance from Pythagoras Theorem. In this case, D (A,B) = proximity(2, (1,1), (5,4)) = 5. 5 3 2 1 A = (1, 1) D(A, B) 5 B=(5, 4) D(A, B)=7 Task: Implement the function proximity(p, A, B) that takes in an integer p. point A and point B (each represented as a tuple of n real numbers). The function should compute and return the value of D (A,B) using the given formula. (Note: the value of dimension n is implicit in the lengths of A and B so there is no need to pass it in as a separate argument.) (20 marks)