How do an element's physical and chemical proper relate to it's position on the periodic table?
The elements in periodic table is never positioned according to only on the basis of physical and chemical properties.
The elements in the periodic table is positioned according to their number of electrons or protons. It is wrong to say that the elements are positioned according to their properties because there are many elements which show relationship with other elements.
For example, Hydrogen which behaves both like halogen and alkali metals.
Lithium is diagonally related with magnesium.
i.e. Carbonate, nitrites, hydroxides of both the elements decomposes on heating and gives the same product.
Due to lanthanum contraction the elements of the period 6 and 7 are almost similar in size.
hence, your assumption is wrong.