Electronegativity measures the ability an atom to attract shared electrons
in bond. It follows a trend that it increases moving from left to right and down to up across
the periodic table.

Ionization energy is the energy required to completely remove an electron from an atom.  The electron that would be removed is the atoms most loosely held electron.  Some atoms are more likely to give up an electron to get to a more stable electron configuration.  This is the reason that Group I elements have the lowest first ionization energy because after loosing one electron, these elements have now acheived an octet configuration. The second ionization energy is the energy to remove a second electron from an atom.  This will be lowest for the Group II elements because these elements acheive an octet configuration after loosing two electrons.  

Atomic radius increases down the columns and to the left. The furthest left elements are Na and Cs. Cs is furthest down so it is the biggest.

Atomic radius expands down the columns and to the LEFT.

Atomic radius INCREASES DOWN and TO THE LEFT in the periodic table

If we look at elements of the same period the prinicipal quantum number for each one of these elements is the same.  Thus the outermost energy level for the electrons of each atom is the same.  If we consider moving through the periodic table in numerical order, the left side of the periodic table features atoms  that have just begun to add electrons to new energy levels.  On the right side of the periodic table the elements are moving closer to filling the energy level.  The differences in atomic radii are the result of differing amounts of protons between atoms whose electrons are in the same energy level.  K has one electron in the fouth energy level and Kr has eight electrons in the fouth energy level.  K has 19 protons with which to generate pull on the electrons.  Kr has 36  protons with which to generate pull on the electrons.  Thus Kr has a smaller atomic radius becasue of its ability to have a tighter grasp on its electrons becasue of the stronger charge generated by its nucleus.  

The trend for radius is that it increases down and to the left

Atomic radius decreases as one moves across the periodic table from left to right, since effective nuclear charge increases and the electrons are held more tightly to the nucleus. 

Effective nuclear charge increases as one moves across a period (row) from left to right, so Cl will have a higher effective nuclear charge. Anions of an element have a lower effective nuclear charge than their parent atom, since they have more electrons than protons and feel less of a pull from the protons in the nucleus. Thus, Cl will have the highest effective nuclear charge. 

Electronegativity increases as one moves left to right across the periodic table, it also increases as one moves up the periodic table. This is because of the changes in the atomic radii of elements that occurs as one move in these directions.  Flourine is the most electronegative element because the positive charge of its nucleus exerts the strongest attractive force on it's electrons when compared to the other elements.  Conversely, the nuclei of the elements in the lower left hand side of the periodic table exert the weakest attractive force on their electrons when compared to the other elements. As one moves from left to right within the same period, one electron and one proton are added to each element.  The electrons will not be any further away from the than the previous element but there will be one more proton with which to generate attractive force on the electrons.  So the upper left hand elements have the most protons within their respective period with which to generate pull on the electrons. The electrons of these species are also the closest in proximity to the nucleii.