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Transformations: cheat sheet

Angles and shapes · The words and methods from the lessons, with an example of each.

translation

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

(x,y)→(x+a, y+b)(x, y) \to (x + a, \, y + b)
A triangle moved 3 right and 2 down
A triangle moved 3 right and 2 down

rotation

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

90∘ anticlockwise: (x,y)→(−y,x)90^\circ \text{ anticlockwise: } (x, y) \to (-y, x)
A triangle turned a quarter turn about the origin
A triangle turned a quarter turn about the origin

reflection

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

x-axis: (x,y)→(x,−y)y-axis: (x,y)→(−x,y)x\text{-axis: } (x, y) \to (x, -y) \qquad y\text{-axis: } (x, y) \to (-x, y)
A triangle reflected in the y-axis
A triangle reflected in the y-axis