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To do this, place the compass tip on the given point on the line. Then, swing the compass, drawing two arcs on both sides of the given point. The arcs should intersect the line. Mark and label the points where the arcs intersect the line.  You can set the compass to any width for this step. For example, you might be given point A on a line. Use the compass to draw point P to the left, and point Q to the right. Place the compass tip on the new point to the left of the original point. Stretch the compass so that it reaches about halfway between the original point, and the new point on the right. For example, place the compass tip on point P, and stretch the compass to a point about halfway between points A and Q. You could also draw the arc below the line. Keeping the compass tip on the left point, swing the compass, drawing an arc. Make sure the arc crosses over the original point. For example, keep the compass tip on point P. Draw an arc above the line. Do not change the width of the compass. Set the compass tip on the right point. Swing the compass, drawing an arc above the line that intersects the first arc. Mark this intersection with another point. For example, place the compass tip on point Q. Draw an arc that intersects the first arc at point T. Use a straightedge to ensure the line is straight. The line you draw is perpendicular to the first line, through the given point on the line. For example, draw a line connecting points A and T.
Draw an arc on either side of the given point. Increase the width of the compass. Draw an arc above the line. Draw a second arc, intersecting the first. Connect the given point to the point where the arcs intersect. Finish up with the construction.