Question

What is the first step in the construction of a line perpendicular to `stackrel(harr)(AB)` and passing through an external point M? Assume that the construction uses only a compass and a straightedge.

Answer 1

To construct a line perpendicular to line AB and passing through an external point M.

Step 1:- Keep point A as center and draw a circle using compass opened with a width equal to radius AM.

Step 2:- Similarly, Keep point B as center and draw another circle using compass opened with a width equal to radius BM.

Step 3:- The two circles drawn so far would cut at two points, first point is M and second point is N.

Step 4:- Join the two points M and N using straightedge.

Step 5:- Therefore, we have a line MN that is perpendicular to line AB.