Question

In step 4 of the construction of a perpendicular line through a point, why must the compass point be placed on the points where the

arc intersects with the original line? How would the construction be different if the compass point were placed at random points on
the original line?

Answer 1

it would miss the point

Explanation:

If the compass point were placed randomly on the line and arcs drawn, you might get a perpendicular by connecting the points where the arcs intersect, but it is not guaranteed to go through the desired point.