The foot of the perpendicular drawn from the point (1,2) to the line x+y=7 is

The perpendicular has direction $(1,1)$, so the foot is $(1+k,2+k)$. Substituting in $x+y=7$ gives $3+2k=7$, so $k=2$ and the foot is $(3,4)$. All four options lie on the line $x+y=7$, so checking the line alone is not enough; the foot must also satisfy that $(1,2)$ and the foot differ by a multiple of the normal $(1,1)$. Only $(3,4)$ does.