(9) The distance from (x, y) to l is the length of line segment which is both perpendicular to l and has one endpoint $P_{1}$ on l and one endpoint $P_{2}$ on (x, y).
Definition of the distance from a point to a line
(10) Because the slope of l is 0, it is a horizontal line.
Definition of a horizontal line
(11) Any line perpendicular to l is vertical.
If a line is perpendicular to a horizontal line, then it is vertical.
(12) All points contained in a line perpendicular to l have the same x-value.