Investigation: Given a line, draw a line perpendicular to the line through point G on the line.
Go to GSP Sketchpad and construct a line and label the two outside points A and B and the inside point G.
Construct a circle on the line using point G as its center and label the two points that intersect the line and circle as points J and K.
Hide your circle. Create a line segment above your drawing and label your endpoints L and M. Place a point on the line and label it N. Highlight point L and N and construct a line segment. This will become the radius of your two circles.
Construct two circles using points J and K as the centers and your radius as line segment LN.
Move point N along line segment LM. Watch your circles get larger. As your circles touch and overlap, place new points at the top and bottom where your two circles intersect.
Use your two new points to create a line segment. Your line segment should pass through point G thus forming a perpendicular line to line AB through point G.