How can I prove start this?I know intuitively since they never meet they are parallel, but I don't think that is a direct proof.
2026-03-30 20:44:25.1774903465
How to prove that given a line L prove that all points of a fixed distance k form two lines parallel to L
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Apply a rotation and then a translation to your line so that it is the axis $y=0$. Then, the distance from a point $(x,y)$ to the line is equal to $\lvert y\rvert$. Hence the points with distance $k$ are the lines $y=\pm k$.