NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Fill in the Blanks

Question 22

Explanation (Very Simple Steps)

Goal: Understand what happens to a 5 cm line segment when it is reflected in a mirror line (line of symmetry).

Key Idea

Reflection is like looking in a mirror. It does not change the shape or the size. It only flips the figure to the other side.

Step-by-Step

1. Start with a segment.
   Call the segment AB.
   Write its length clearly:
   ( overline{AB} = 5 ext{ cm} )
2. Draw the mirror line.
   Let the mirror (line of symmetry) be ( l ).
3. Reflect each endpoint.
   Point A goes to a new point A′ on the other side of ( l ).
   Two important facts for a reflection:
   ( overline{AA'} perp l )
   and distances to the mirror are equal:
   ( ext{dist}(A, l) = ext{dist}(A', l) ).
   
   Do the same for point B to get B′:
   ( overline{BB'} perp l )
   and ( ext{dist}(B, l) = ext{dist}(B', l) ).
4. Join the reflected points.
   Draw the segment ( overline{A'B'} ). This is the image of ( overline{AB} ).
5. Compare lengths.
   Reflection is a rigid motion (it does not stretch or shrink).
   So lengths stay the same:
   ( overline{A'B'} = overline{AB} ).
   We already know ( overline{AB} = 5 ext{ cm} ).
   Therefore,
   ( overline{A'B'} = 5 ext{ cm} ).

Conclusion

The reflection (image) of a 5 cm line segment is also a line segment of length 5 cm.
In short: a line segment of length 5 cm.

Answer (for the fill-in-the-blanks)

a Line segment of length 5 cm.

Why this is true: Reflection keeps distances equal and preserves shape and size, so the image is congruent to the original segment.