Geometric constructions: perpendicular line through a point on the line

Construct a line perpendicular to the given line. So if I can pick two arbitrary points on this line, and if I can make a line that is always equidistant from those two points, then that line will be perpendicular. And actually, it will be a perpendicular bisector of the segment formed by those two points. Now, they don't care whether we're bisecting anything. But they do care about it being perpendicular. So let's do this. So I'm going to draw a circle with my compass. And so let's just pick that point right over there. I could adjust the radius if I like. But I might as well-- well, I'll just leave it right over there. Now let me draw another circle. And this time, I'm going to center it where the first circle intersects with my line. And then I'm going to adjust the radius to overlap with the first dot. And now, where these two circles intersect, those are points that are equidistant from both of these centers that I just constructed. So let me draw a line that connects those two. And that line is going to be perpendicular to our original line.