There are three kinds of ** isometric changes ** of 2 -dimensional shapes: translations, rotations, and also reflections. ( * Isometric * means that the change doesn"t change the dimension or form of the figure.) A fourth kind of transformation, a ** dilation ** , is not isometric: that preserves the shape of the figure yet not that is size.

## Translations

A ** translate in ** is a ** sliding ** the a figure. For example, in the figure below, triangle A B C is translated 5 systems to the left and also 3 systems up to obtain the ** image ** triangle A " B " C " .

This translation have the right to be described in name: coordinates notation as ( x , y ) → ( x − 5 , y + 3 ) .

## Rotations

A second type of change is the ** rotation ** . The figure below shows triangle A B C rotated 90 ° clockwise around the origin.

This rotation can be described in name: coordinates notation together ( x , y ) → ( y , − x ) . (You can examine that this works by plugging in the collaborates ( x , y ) of every vertex.)

## reflections

A third form of revolution is the ** enjoy ** . The figure listed below shows triangle A B C reflected throughout the line y = x + 2 .

This reflection can be explained in coordinate notation as ( x , y ) → ( y − 2 , x + 2 ) . (Again, girlfriend can inspect this through plugging in the collaborates of every vertex.)

## Dilations

A ** dilation ** is a revolution which conservation the shape and also orientation that the figure, yet changes that is size. The ** scale factor ** of a dilation is the factor whereby each direct measure that the number (for example, a side length) is multiplied.

The figure listed below shows a dilation with scale element 2 , focused at the origin.

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This dilation can be defined in name: coordinates notation as ( x , y ) → ( 2 x , 2 y ) . (Again, you can inspect this by plugging in the works with of each vertex.)