Translations and Rotations

Translation – a transformation of a figure in which each point is moved the same distance in the same direction (also known as a slide).

*The image of P(x, y) under a translation a units horizontally and b units vertically is given by:

P(x, y) –>  P'(x + a, y + b)

**When you:

add to the x, you are moving to the right along the x-axis

subtract from x, you are moving to the left along the x-axis

add to the y, you are moving up the y-axis

subtract from the y, you are moving down the y-axis

Ex: translate P(-2, 4) to the right 5 units and down 3 units, the image will be:

P(-2,4) –> P'(-2 + 5, 4 + (-3)) = P'(3,1)

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Rotation – a transformation involving turning of a figure or point.

We will only look at rotations about the origin. Memorize these:

*Rotation of 90° about the origin (x, y) –> (-y, x)

*Rotation of 180° about the origin (x, y) –> (-x, -y)

*Rotation of 270° about the origin (x, y) –> (y, -x)