AQR Section 37: Taxicab Distance v. Euclidean Distance

Drag points A and B along the blue lattice grid. Observe how the Taxi Distance and the Euclidean Distance change. Under what conditions is the Taxi Distance equal to the Euclidean Distance? Under what conditions is the Taxi Distance less than the Euclidean Distance? Under what conditions is the Taxi Distance greater than the Euclidean Distance?