Transformations and enlargement
See which transformations keep lengths, angles and orientation, enlarge a shape from a centre by 2 and by 12, find the centre of an enlargement, and see what happens to the area.
- UK: Year 8
- France: grade 9
- Germany: grade 9
- Iran: grade 7
- Afghanistan: grade 9
- Syria: grade 7
- Ukraine: grade 9
- Russia: grade 9
Guide
This studio is for Year 8 (KS3: properties of translations, rotations and reflections; similar shapes by enlargement, with and without coordinate grids). Iran teaches the three moves in Year 7 and enlargement («تجانس») later; the Afghan books teach the three moves in grade 9.
A translation, a reflection and a rotation move a shape without changing its side lengths or angles: the image is congruent to the shape. Only a reflection reverses the orientation: if the vertices A, B, C go round anticlockwise, in the mirror image they go round clockwise, just as your right hand looks like a left hand in a mirror.
In an enlargement with centre O and scale factor k, every point stays on its ray from O and its distance from O is multiplied by k. Measure from the centre, not from the shape. A factor bigger than 1 makes the shape bigger; a factor between 0 and 1, such as 12, makes it smaller. Angles do not change, so the image is similar to the shape.
When lengths are multiplied by k, the area is multiplied by k × k: with factor 3 the area is 9 times as big, not 3 times.