prof. ng notes that we don't necessarily have to split on the x axis, then the y axis, etc (on average this tends to be good so we don't end up with "strips") in a golden ratio spiral fashion. instead, we can test to see which axis gives us the best split, i.e by the number of objects on each side of the split.
Sorry, I’m having some trouble understanding the figure and how the labels ABCD are determined
ABCD are the split locations, so A splits the first box into space (1) and (2, 3, 4, 5). Then, B splits (2, 3, 4, 5) into (2) and (3, 4, 5). Then, C splits (3, 4, 5) into (3) and (4, 5), etc. The tree structure on the right is another way of expressing this.