Transformations
7.1 Transformations – Cheat Sheet
| Transformation Type | Definition / Rule | Example / Notes |
|---|---|---|
| Reflection | A flip of a shape in a mirror line. Each point and its image are the same perpendicular distance from the mirror line. | Mirror lines can be x-axis, y-axis, y = x, y = −x, or any vertical/horizontal/diagonal line. |
| Rotation | Turning a shape about a fixed centre through a given angle. | Common angles: 90°, 180°, 270° (clockwise or anticlockwise). Described by: “Rotation, centre (x, y), angle, direction.” |
| Enlargement | Changing the size of a shape from a fixed centre by a given scale factor (k). | If k > 0 → image same orientation; if k < 0 → image rotated 180°. k > 1 → enlargement; 0 < k < 1 → reduction; k < 0 → enlargement with rotation. |
| Translation | Sliding a shape without turning or flipping it. Described by a vector: ( x , y ). | Positive x → right; Negative x → left; Positive y → up; Negative y → down. |
Transformation Properties Table
| Transformation | Changes Shape Size? | Changes Orientation? | Preserves Lengths & Angles? | Isometry? |
|---|---|---|---|---|
| Reflection | No | Yes (flips) | Yes | Yes |
| Rotation | No | Yes (rotates) | Yes | Yes |
| Enlargement | Yes (unless k = 1) | No if k > 0, Yes if k < 0 | No | No |
| Translation | No | No | Yes | Yes |
Vector Notation for Translation
- Written as column vector:
( x )
( y )
where x = horizontal movement, y = vertical movement.
Example: ( 3 ) ( −2 ) means 3 units right, 2 units down.