The left half of a cross-shaped figure is drawn on a square grid. The dotted vertical line is the line of symmetry. The left half shows: - A horizontal arm: 3 squares wide (extending left from the axis) and 1 square tall - A vertical strip at the axis: 1 square wide and 3 squares tall (1 square above and 1 square below the horizontal arm) The figure is completed by reflecting the left half across the dotted line. How many lines of symmetry does the completed figure have in total?
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Worked Solution
Step 1: Complete the figure by reflecting the left half.
The completed cross:
- Total width: 3 squares (left arm) + 3 squares (right arm) = 6 squares
- Total height: 3 squares
- Centre strip: 2 squares wide, 3 squares tall
- Horizontal arms: 6 squares wide, 1 square tall
Step 2: Test for vertical symmetry (fold left and right).
Left arm mirrors right arm.
Step 3: Test for horizontal symmetry (fold top and bottom).
The 1 square above the arm equals the 1 square below.
Step 4: Test for diagonal symmetry.
Horizontal reach = 3 squares, vertical reach = 1 square. These are unequal.
Reflecting across a diagonal does NOT map the cross onto itself.
Step 5: Total lines of symmetry = 2 (vertical + horizontal)
Correct answer: 2
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