Combine translations, reflections and turns, and explain tiling without gaps.
Example 1
Two copies of any triangle can be joined by a 180∘ turn about the midpoint of one side to make a parallelogram. How can this help tile the plane?
Show worked answer
Answer: Translate copies of the parallelogram in rows to fill the plane.
A half-turn joins the pair of triangles into a parallelogram.
Repeated translations of that parallelogram fit opposite parallel edges together, creating a tessellation with no gaps or overlaps.
Example 2
One corner of a tile is at (1,2). Translate the tile 3 units right and 1 units up, then reflect it in the vertical y−axis. Where is that corner now? Give (x,y).
Tile corner before transformationsShow worked answer
Answer: (−4,3)
Translation gives (4,3).
Reflection in the y−axis reverses the horizontal coordinate and keeps the vertical coordinate: (−4,3).
Example 3
A tile corner starts at (3,4). Rotate it 90∘ clockwise about the origin, then translate it 2 units right. What are the final coordinates (x,y)?
Tile corner before turningShow worked answer
Answer: (6,−3)
A 90∘ clockwise rotation about the origin changes (x,y) to (y,−x), giving (4,−3).
Moving 2 right adds 2 to the first coordinate: (6,−3).
Transformations and tessellations practice | Year 6 | Ascent Arcade