What is Euclidean And Manhattan distances in KNN?

Euclidean Distance:

• Euclidean distance is calculated as the square root of the sum of the squared differences between a new point (x) and an existing point (y).
• The Euclidean distance or Euclidean metric is the "ordinary" (i.e. straight-line) distance between two points in the Euclidean space. 
• The Euclidean distance between points p and q is the length of the line segment connecting them.  

Manhattan Distance:

• This is the distance between real vectors using the sum of their absolute difference.
• It is the sum of the lengths of the projections of the line segment between the points onto the coordinate axes. 

Formulae to calculate different distances between two points (x1, y1), and (x2, y2):