Dependency of locus sets on the initial construction 2
- Zoltán Kovács
Consider a triangle ABC, free point D and the lines f, g through D perpendicular to the sides AC and BC of the triangle. When are these lines perpendicular? Drag point D to find a correct position.
After some attempts it is clear that this is impossible. The angle is determined by the initial position of the triangle. On the other hand, if the triangle is right (the angle at C is right), then all positions of D will succeed. Let us try the obtain the same result by using the
LocusEquation[ArePerpendicular[f,g],D]command in GeoGebra. When 0=-1 is displayed in the Algebra View, it means that there is no possible position for D when assuming an initial construction. By contrast, when 0=0 is displayed, it means that all positions of D will satisfy the condition.