Part (a)
In the given case, when a dog walk along a sidewalk then the co-ordinate system is one dimenstional as it walk along a straight line.
Part (b)
When an acrobat walk along a high wire then its co-ordinate system is also one dimensional as it does not move in any other direction.
Part (c)
When a submerging submarine makes an angle with the horizontal then the co-ordinate system of the condition is two dimensional as it will also make some angle with the vertical axis.
Part (d)
When a person climb a ladder at an angle then its co-ordinate system is also two dimentsional as it make angle with the ground similarly it will some angle with the vertical.