For drawing a perpendicular line from a point outside the line can we do it in the following fashion

Draw line L. Take a point P outside it. Draw an arc from P cutting line AB. Then approaching differently take a distance of more than half of AB and draw two arcs in the same side as P (my son did it this way in his test). This is different from your approach since it doesnt take the same radius as the arc from P cutting AB. Even here when you connect P to the connecting point of two arcs and extend it to the line, you get a perpendicular line from P to line L. Isnt this correct?

Dear Student

 
The approach taken by you gives the perpendicular bisector of the given line segment AB. If we take any point on the perpendicular bisector, the line through it would be perpendicular to the line segment. But, the given point P may not always lies on the perpendicular bisector.
This is about the construction of the perpendicular bisector of AB.
 Hope this helps!
 
Cheers!

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