---
title: "Transformations: cheat sheet"
subtitle: "Angles and shapes"
---

# Transformations

> The words and methods from this unit, with an example of each.

:::keep-together

**translation**: Every point slides the same way. Right and up add; left and down take away.

$$(x, y) \to (x + a, \, y + b)$$

_A triangle moved 3 right and 2 down_

:::

:::keep-together

**reflection**: Each point and its image are the same distance from the mirror, on opposite sides.

$$x\text{-axis: } (x, y) \to (x, -y) \qquad y\text{-axis: } (x, y) \to (-x, y)$$

_A triangle reflected in the y-axis_

:::

:::keep-together

**rotation**: Give the centre, the angle and the direction. A half turn: (x, y) to (−x, −y). 90° clockwise is 270° anticlockwise.

$$90^\circ \text{ anticlockwise: } (x, y) \to (-y, x)$$

_A triangle turned a quarter turn about the origin_

:::