Question

Draw the perpendicular bisector of `overline"XY"` whose length is 10.3 cm.

1. Take any point P on the bisector drawn. Examine whether PX = PY

2. If M is the midpoint of `overline"XY"`, what can you say about the lengths MX and XY?

Answer 1

1. Draw a line segment `overline"XY"` of 10.3 cm.
   
2. Taking point X as centre, draw a circle by using compasses. The radius of circle should be more than half the length of `overline"XY"`.  
   

3. With the same radius as before, draw another circle using compasses while taking point Y as centre. Let it cut the previous circle at A and B. 

   

4. Join `overline"AB"`. `overline"AB"` is the axis of symmetry. 
   

1. Take any point P on `overline"AB"`. We will find that the measures of the lengths of PX and PY are same.

   It is because `overline"AB"` is the axis of symmetry. Hence, any point lying on `overline"AB"` will be at the same distance from both the ends of `overline"XY"`.
   

2. M is the mid-point of `overline"XY"`. Perpendicular bisector `overline"AB"` will be passing through point M. Hence, the length of `overline"XY"` is just double of `overline"MX"`.

   Or 2MX = XY