Background reading · Mathematics and Statistics
Moving shapes: transformations and symmetry
The four ways to move or change a shape on a grid, what they do to coordinates, and how to describe the symmetry of a pattern.
A transformation moves or changes a shape. Designers use transformations to turn one small tile into a whole floor, and animators use them to move characters across a screen.
The four transformations
The first three keep the shape exactly the same size. Mathematicians call the copies congruent. An enlargement keeps the same shape but changes the size. Those copies are called similar.
Transformations with coordinates
On a four-quadrant grid, transformations make patterns in the numbers. Reflect the point (3, 2) in the y-axis and it becomes (−3, 2): the x-coordinate changes sign. Rotate (3, 2) by 180° about (0, 0) and it becomes (−3, −2). Enlarge (3, 2) by scale factor 2 from (0, 0) and it becomes (6, 4).
A surprise about area
When you enlarge a shape by scale factor 2, the sides double but the area becomes four times bigger, because both the length and the width double. With scale factor 3 the area is nine times bigger. That matters when you order tiles for a real courtyard.
Symmetry
A shape or pattern has line symmetry if you can fold it along a line so both halves match. It has rotational symmetry if it looks the same after turning less than a full turn. The number of times it looks the same in one full turn is its order of rotational symmetry. A square has 4 lines of symmetry and rotational symmetry of order 4.
Sources and further reading
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