Question

Given two objects represented by the tuples (22, 1, 42, 10) and (20, 0, 36, 8):(a)Compute the Euclidean distance between the two objects. (b) Compute the Manhattan distance between the two objects.

Answer 1

Answer:

(a) 6.708

(b) 11

Step-by-step explanation:

Tuples ( 22, 1, 42, 10) and (20, 0, 36, 8)

Euclidian distance formula  

$D = \sqrt{(q1 -p1)^2 + (q2-p1)^2 + (q3 - p3)^2 + (q4 -p4)^2}$

D = $\sqrt{(22-20)^2 + (1-0)^2 + (42 -36)^2 + (10 -8)^2 }$

   = $\sqrt{(2)^2 + (1)^2 + (6)^2 + (2)^2}$

    = $\sqrt{4 + 1 + 36 + 4 }$

     = $\sqrt{45}$

 D    = 6.708

Therefore the Euclidean distance between the tuples is 6.708

Manhattan Distance formula

D = |q1-p1| + |q2 -p2| + |q3 -p3| + |q4-p4|

  = |22-20| + | 1-0| + | 42 -36| + | 10-8|

 = |2| + |1| + |6| + |2|

D = 11

Therefore the Manhattan distance is equal to 11