After doing this	Your work should look like this
Start with a line and point K on that line.
1.  Set the compass width to a medium setting. The actual width does not matter.
2.  Without changing the compass width, mark a short arc on the line at each side of the point K, forming the points P,Q. These two points are thus the same distance from K.
3.  With the compass on P, set its width to any setting beyond K.
4.  Mark off an arc on one side of the line.
5.  Without changing the compass width repeat from the point Q so that the the two arcs cross each other, creating the point R
6.  Using the straight edge, draw a line from K to where the arcs cross.
7.  Done. The line KR just drawn is a perpendicular to the line PQ at K

Proof

This construction works by effectively building two congruent triangles. The image below is the final drawing above with the red lines added.

Constructions pages on this site

Lines

• Introduction to constructions
• List of printable constructions worksheets
• Copy a line segment
• Perpendicular bisector of a line segment
• Perpendicular from a line at a point
• Perpendicular from a line through a point
• Perpendicular from endpoint of a ray
• Divide a segment into n equal parts
• Parallel line through a point (angle copy method)
• Parallel line through a point (rhombus method)

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Equilateral triangle
• Triangle medians
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two sides and included angle (sas)
• Incircle of a triangle
• Circumcircle of a triangle

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Focus points of a given ellipse

Polygons

• Hexagongiven one side
• Hexagon inscribed in a given circle
• Pentagon inscribed in a given circle

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object