An ant is moving on the cooridnate plane, starting form point (0,ā1) along a straight line until it reaches the x- axis at point (x,0) where x is a real number. After it turns 90o 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 90o 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 answersPS. Collected [url=https://artofproblemsolving.com/community/c949609_2019_nigerian_senior_mo_round_4]here analytic geometrydistancebroken linerationalaxescoordinatecombinatorics