MathDB

An ant is moving on the cooridnate plane, starting form point

(0,-1)

along a straight line until it reaches the

x

- axis at point

(x,0)

where

x

is a real number. After it turns

90^o

to the left and moves again along a straight line until it reaches the

y

-axis . Then it again turns left and moves along a straight line until it reaches the

x

-axis, where it once more turns left by

90^o

and moves along a straight line until it finally reached the

y

-axis. Can both the length of the ant's journey and distance between it's initial and final point be: (a) rational numbers ? (b) integers? Justify your answers
PS. Collected [url=https://artofproblemsolving.com/community/c949609_2019_nigerian_senior_mo_round_4]here

Problem Statement