Let x, y ∈ R2 be two points in the plane. As usual, denote their coordinates by x1 and x2, and y1 and y2, respectively. The Euclidean distance between these points is the length of the line that...

Let x, y ∈ R2 be two points in the plane. As usual, denote their coordinates by x1 and x2, and y1 and y2, respectively. The Euclidean distance between these points is the length of the line that connects them: p (x1 − y1) 2 + (x2 − y2) 2 . The Manhattan distance between them is |x1 − y1| + |x2 − y2|: the number of blocks that you would have to walk “over” plus the number that you’d have to walk “up” to get from one point to the other. Denote these distances by deuclidean and dmanhatta

1.Prove that deuclidean(x, y) ≤ dmanhattan(x, y) for any two points x, y.

2.Prove that there exists a constant a such that both