Subjects geometry

Pattern Symmetry

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Pattern Symmetry


1. **Problem Statement:** Determine the number of lines of symmetry in a 7x7 grid pattern with black squares at specified positions. 2. **Understanding Symmetry:** A line of symmetry divides a figure into two mirror-image halves. Common symmetry lines in grids are vertical, horizontal, and diagonal lines. 3. **Given Pattern:** Black squares are at: - Row 2: columns 2, 4, 5, 7 - Row 4: columns 1, 2, 4, 5, 7 - Row 6: columns 2, 4, 5, 7 4. **Check Vertical Symmetry:** The pattern is symmetrical about the vertical line between columns 4 and 5. This means the left half mirrors the right half. 5. **Check Horizontal Symmetry:** The pattern is symmetrical about the horizontal line between rows 4 and 5. The top half mirrors the bottom half. 6. **Check Diagonal Symmetry:** For diagonal symmetry, the pattern would need to mirror along the main diagonals. Given the positions, the pattern does not exhibit diagonal symmetry. 7. **Conclusion:** The pattern has exactly 2 lines of symmetry: one vertical and one horizontal. **Final answer:** The pattern has **2** lines of symmetry.