Constructing a perpendicular line

After doing thisYour 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 1Place the compasses on the given external point R.Geometry construction with compass and straightedge or ruler or ruler or ruler
Step 2Set 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 3Draw 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 QGeometry construction with compass and straightedge or ruler or ruler or ruler
Step 4At 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 5Place 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 6Done. 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

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