There space three kinds of ** isometric revolutions ** of 2 -dimensional shapes: translations, rotations, and also reflections. ( * Isometric * means that the transformation doesn"t adjust the size or form of the figure.) A fourth kind of transformation, a ** dilation ** , is no isometric: it preserves the shape of the figure but not the size.

## Translations

A ** translate into ** is a ** sliding ** of a figure. Because that example, in the figure below, triangle A B C is analyzed 5 units to the left and also 3 systems up to get the ** image ** triangle A " B " C " .

This translation can be explained in coordinate notation as ( x , y ) → ( x − 5 , y + 3 ) .

## Rotations

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

This rotation have the right to be described in name: coordinates notation as ( x , y ) → ( y , − x ) . (You can check that this works by plugging in the works with ( x , y ) of each vertex.)

## reflections

A third kind of change is the ** have fun ** . The figure below shows triangle A B C reflected across the heat y = x + 2 .

This reflection deserve to be explained in name: coordinates notation as ( x , y ) → ( y − 2 , x + 2 ) . (Again, you can check this by plugging in the coordinates of every vertex.)

## Dilations

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

The figure below shows a dilation v scale aspect 2 , focused at the origin.

You are watching: The original figure in a transformation

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