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Constructing a perpendicular to a line through a point

This is the step-by-step, printable version. If you PRINT this page, any ads will not be printed.

See also the animated version.

  After doing this Your work should look like this
  Start with a line and point R which is not on that line. Geometry construction with compass and straightedge or ruler or ruler or ruler
Step 1 Place the compasses on the given external point R. Geometry construction with compass and straightedge or ruler or ruler or ruler
Step 2 Set the compasses' width to a approximately 50% more than the distance to the line. The exact width does not matter. Geometry construction with compass and straightedge or ruler or ruler or ruler
Step 3 Draw an arc across the line on each side of R, making sure not to adjust the compasses' width in between. Label these points P and Q Geometry construction with compass and straightedge or ruler or ruler or ruler
Step 4 At this point, you can adjust the compasses' width. Recommended: leave it as is.

From each point P,Q, draw an arc below the line so that the arcs cross.
Geometry construction with compass and straightedge or ruler or ruler or ruler
Step 5 Place a straightedge between R and the point where the arcs intersect. Draw the perpendicular line from R to the line, or beyond if you wish. Geometry construction with compass and straightedge or ruler or ruler or ruler
Step 6 Done. This line is perpendicular to the first line and passes through the point R. It also bisects the segment PQ (divides it into two equal parts) Geometry construction with compass and straightedge or ruler or ruler or ruler

Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions