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Test: Symmetry and transformations

Dynamic tasks about lines of symmetry, reflection, central symmetry, rotation and translation. The test develops the ability to recognise and apply geometric transformations.

Question qty: 10
Duration in minutes: 12
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Sample questions

  • Which direction will the arrow point after a kampas° clockwise rotation? rodykle
  • Point A(x; y) is translated dx squares to the right and dy squares up. What are its new coordinates?
  • Point A(x; y) is reflected in the centre O(5; 5). What are the coordinates of the new point?
  • Which shape has a lines of symmetry?
  • How many lines of symmetry does the shown shape have?
  • Point A is reflected in the vertical line x = 5. What are the coordinates of the reflected point?
  • Through what clockwise angle should the first arrow be rotated to obtain the second? a  →  b
  • Which transformation is shown?

Symmetry and geometric transformations

A shape has line symmetry if it can be folded along a line so that both parts coincide. When a point is reflected across a line of symmetry, its perpendicular distance from the line remains equal on both sides.

Types of transformation

  • A reflection flips a shape across a mirror line.
  • A translation moves every point in the same direction and by the same distance.
  • A rotation turns a shape around a centre through a stated angle.
  • Central symmetry is equivalent to a 180° rotation.

These transformations preserve side lengths, angles and area. Only position or orientation changes. In coordinate tasks, verify the movement of every vertex separately.

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