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AQA GCSE · Question 03 · Geometry and Measures
In the grid below, shade one quarter of the squares so that the grid has exactly two lines of symmetry. Shade complete squares only.
In the grid below, shade one quarter of the squares so that the grid has exactly two lines of symmetry. Shade complete squares only.
How to approach this question
1. Calculate how many squares represent "one quarter" of the total grid. The grid is 4x4, so there are 16 squares in total.
2. Determine the number of squares to shade: (1/4) * 16.
3. Identify the possible lines of symmetry in a 4x4 grid (horizontal, vertical, and two diagonals).
4. Experiment with shading the calculated number of squares to find a pattern that has exactly two lines of symmetry.
Full Answer
The grid is 4x4, so it has 16 squares.
One quarter of the squares is 1/4 * 16 = 4 squares.
We need to shade 4 squares.
For the grid to have exactly two lines of symmetry, these lines must be the horizontal and vertical lines through the middle of the grid. Shading the four central squares achieves this.
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<br>
<svg width="700" height="700" viewBox="0 0 150 150" xmlns="http://www.w3.org/2000/svg">
<title>Answer Grid</title>
<defs>
<style>.cell { stroke: black; stroke-width: 1; fill: none; } .shaded { fill: #808080; }</style>
</defs>
<rect class="cell" x="25" y="25" width="25" height="25" />
<rect class="cell" x="50" y="25" width="25" height="25" />
<rect class="cell" x="75" y="25" width="25" height="25" />
<rect class="cell" x="100" y="25" width="25" height="25" />
<rect class="cell" x="25" y="50" width="25" height="25" />
<rect class="cell shaded" x="50" y="50" width="25" height="25" />
<rect class="cell shaded" x="75" y="50" width="25" height="25" />
<rect class="cell" x="100" y="50" width="25" height="25" />
<rect class="cell" x="25" y="75" width="25" height="25" />
<rect class="cell shaded" x="50" y="75" width="25" height="25" />
<rect class="cell shaded" x="75" y="75" width="25" height="25" />
<rect class="cell" x="100" y="75" width="25" height="25" />
<rect class="cell" x="25" y="100" width="25" height="25" />
<rect class="cell" x="50" y="100" width="25" height="25" />
<rect class="cell" x="75" y="100" width="25" height="25" />
<rect class="cell" x="100" y="100" width="25" height="25" />
</svg>
Common mistakes
✗ Shading the wrong number of squares (e.g., shading one quarter of the area visually without counting).
✗ Creating a pattern with one line of symmetry (e.g., shading the top row only).
✗ Creating a pattern with four lines of symmetry (e.g., shading the four central squares AND the four corner squares).
✗ Creating a pattern with rotational symmetry but no lines of reflectional symmetry.
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