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

Question 71

Answer (short)

Copy (reflect) the given half across line l. The mirror image completes the figure so that it is symmetric about l.

Explanation — step by step

1. Understand the goal. We want line l to be the line of symmetry. That means the whole figure should look the same on both sides of l.
2. Mark key points on the given half. Pick corners, endpoints of edges, and any sharp bends on the drawn half.
3. Drop a perpendicular to the line. For each chosen point (P), draw a short line from (P) to l so that it meets l at a right angle.

   (overline{PP_perp} perp l)

4. Measure the distance to the line. Note the perpendicular distance from (P) to l.

   (d(P,l))

5. Place the mirror point on the other side. On the same perpendicular line, mark point (P') on the opposite side of l so that the distance is equal.

   (d(P',l) = d(P,l))

   (overline{PP'} perp l)

6. Repeat for all key points. Do this for every important point you marked in step 2.
7. Connect the mirrored points. Join the new points (P') in the same order and with the same kinds of lines (straight or curved) as on the original half. This draws the mirror image.
8. Handle points on the line. Any point that lies exactly on l stays where it is (it is its own mirror).

   (P in l ;Rightarrow; P' = P)

9. Final check for symmetry. For any pair of matching points (P) and (P'):

   (d(P,l) = d(P',l))

   (angle(PP',l) = 90^circ)

   If both are true, your figure is symmetric about l.

Quick tips

• Use a ruler and a set square (or a right-angle edge) to draw clean perpendiculars.
• Match shapes as well as distances — straight edges match straight edges, curves match curves.
• If something looks “shifted”, recheck the perpendicular direction and the equal distance.