NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Problems and Solutions

Question 74

Step-by-step (Beginner Friendly)

1. Understand the goal
   

   We want the whole figure to look the same on both sides of the line l. The line l is the mirror.

   \(\text{line } l = \text{axis of symmetry}\)

2. Pick a corner (vertex)
   

   Choose any visible corner point on the given half. We will copy this point to the other side of l.

3. Drop a perpendicular to the line
   

   From the chosen point, draw a short line to l that meets l at a right angle.

   \(\overline{PA} \perp l\)

   \(\angle PAl = 90^\circ\)

4. Measure the distance to the line
   

   Note how far the point is from the line l along this perpendicular.

   \(d = \text{distance}(P,\ l)\)

5. Mark the mirror point on the other side
   

   On the same perpendicular, mark a point at the same distance on the other side of l.

   \(\text{If } \overline{PA} = d, \text{ then choose } P' \text{ on the other side with } \overline{AP'} = d\)

   \(\Rightarrow P' \text{ is the reflection of } P \text{ in } l\)

6. Repeat for all corners
   

   Do the same perpendicular-and-equal-distance process for every vertex on the given half.

7. Join the reflected points
   

   Connect the new points in the same order as the original half (straight lines with straight lines, curves with curves) to complete the figure.

Quick Checks

• Each original point and its mirror point should be equally far from l.
• The joining segment between a point and its mirror should be perpendicular to l.
• After joining all, the left and right parts should overlap if folded on l.

Why this works

Reflection in a line keeps the distance to that line the same and flips the point to the opposite side.