2.6 Drop a Perpendicular

Instruction: Drop a perpendicular from the point to the line.

Goal: 2L 3E

Available tools:

• Move
• Point
• Line
• Circle
• Perpendicular Bisector
• Angle Bisector
• Intersect

Pack: Beta

Previous level: 2.5

Next level: 2.7

2L solution

Let O be the point.

1. Construct a circle with center O and an arbitrary radius so that it intersects the line at two points A and B
2. Construct the perpendicular bisector of AB

3E solution

Let O be the point.

1. Construct a circle with an arbitrary center A on the line and radius OA
2. Construct a circle with center B at intersection of circle A and the line and radius OB, intersecting circle A at C
3. Construct line OC

Explanation

Solution 2L has you construct an arbitrary isosceles triangle ABO with O as its apex. The perpendicular bisector of its base will pass through its apex and therefore will answer the puzzle.

Solution 3E has you construct the reflection of point O through the line, making that line the perpendicular bisector of the segment joining point O to its reflection. Just trace that segment.