The figure below shows 12 identical squares. What is the least number of such squares that must be added to the figure so that the line becomes a line of symmetry?

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Worked solution
7
1. Identify the reflection of each column across the line of symmetry $AB$.
For the line to be a line of symmetry, every square above must have a corresponding square below at the same distance, and vice versa.
- Row U1 reflects to Row D1.
- Row U2 reflects to Row D2.
2. Determine the missing squares in each column.
- Column 1: Has a square at U1, so it needs a square at D1 ( square needed).
- Column 2: Has squares at U2, U1, D1, D2. It is already symmetric.
- Column 3: Has squares at U2, U1, D1, D2. It is already symmetric.
- Column 4: Has squares at U1, D1. It is already symmetric.
- Column 5: Has a square at D1, so it needs a square at U1 ( square needed).
3. Calculate the total number of squares to be added.
Total squares to add .
Answer
(option 2)
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