Transformations
Translations, rotations, reflections, and dilations โ the four fundamental ways to move or resize figures while preserving structure.
A transformation moves or changes a shape in a predictable way. The original shape is called the pre-image; the result is called the image.
There are four basic transformations:
- Translation: slides a shape in a straight line โ every point moves the same distance in the same direction
- Rotation: turns a shape around a fixed point (the centre of rotation) by a given angle
- Reflection: flips a shape across a line (the line of reflection), producing a mirror image
- Dilation: enlarges or shrinks a shape by a scale factor relative to a fixed point
The first three โ translation, rotation, and reflection โ are called rigid motions or isometries because they preserve distances and angles. The shape changes position but not size or shape.
The triangle with vertices , , is translated units right and unit down.
Add to each vertex:
Reflect the point across the -axis. Then reflect it across the -axis.
Solution
Reflection across the -axis: negate the -coordinate. .
Reflection across the -axis: negate the -coordinate. .