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

Question 18

1. What is a mirror line?
   A mirror (line of symmetry) is a straight line. When you reflect a point across this line, you get its image on the other side.
2. How do we measure distance to a line?
   We always measure the shortest distance from a point to a line. This shortest distance is along a perpendicular.
   Write the idea in math steps:

   ( ext{Let the mirror be the line } L. )

   ( ext{Let the point be } P. )

   ( ext{Draw } PQ perp L. )

   ( ext{Then the distance from } P ext{ to } L ext{ is } |PQ|. )
3. Where is the image placed?
   The image of ( P ) lies on the same perpendicular we drew, but on the other side of the mirror line.
   Math steps:

   ( ext{Mark a point } P' ext{ on the line } PQ ext{ such that } Q ext{ is between } P ext{ and } P'. )

   ( ext{Also, make } |QP'| = |QP|. )
4. Key symmetry property
   In reflection, the mirror line is the perpendicular bisector of the segment joining the point and its image.
   Math steps:

   ( Q ext{ is the midpoint of } PP'. )

   ( L perp PP'. )
5. Conclude the distances
   Since ( |QP| = |QP'| ),
   ( ext{distance of object from mirror} = |QP|, )
   ( ext{distance of image from mirror} = |QP'|. )
   Therefore,
   ( |QP| = |QP'| Rightarrow ) the distances are the same.

Quick Number Example

If the object is at a perpendicular distance of ( 3 ext{ cm} ) from the mirror, then the image is also at ( 3 ext{ cm} ) on the other side of the mirror.

Common Mistakes to Avoid

• Do not measure slanted distance; always use the perpendicular to the mirror.
• Remember, the image lies on the same perpendicular line as the object, just across the mirror.

One-Line Reason (for revision)

In reflection in a line, the line acts as a perpendicular bisector of the segment joining a point and its image, so their perpendicular distances from the mirror are equal.