The reason for this trend is because the atoms further along the period are more likely to gain electrons to fill their valence shell rather than lose them. This is because across the period the first ionisation energy increases, as the higher core charge results in significant attraction between the nucleus and outer electrons, making it more difficult to remove them. As metals gain their reactivity by losing their electrons, the increased first ionisation energy across the period does not allow for this, and so metals are located at the start of the period where the first ionisation energy is lower. In addition, the higher electronegativity towards the end of the period corresponds with the non-metals, due to their increased ability to attract and gain electrons to complete their outer shell.
As you move across the period, the Period 3 elements' reactivities with water decreases. This is evident because the first element in period 3, sodium, reacts very violently with water; igniting vigorously to form a pink flame, whereas sulfur, which is located further along the period, merely demonstrated no visible reaction at all. This is due to the increased core charge across the period, which results in increased first ionisation energy. This makes it more difficult for the elements further along the period to lose their electrons, therefore accounting for the minimal