Transformations in math happen when over there is a adjust in position, shape, or size. As soon as you are playing with a jigsaw puzzle, you can move a puzzle piece by slide it, flipping it, or turning it.

Each of these moves is a transformation of the puzzle piece.

You are watching: A dilation is a transformation whose preimage and image are

In a transformation, the original number is a preimage and also the resulting figure is one image.

A revolution is one isometry if the preimage and also the image are congruent. Is the change below one isometry?


Since the revolution involves a change in size, the is not an isometry. The political parties of the preimage triangle and the political parties of the photo triangle space not congruent or equal.

Types of revolutions in math

TranslationA translation or slide is one isometry in which all points of a number move the very same distance and also in the same direction.


ReflectionA reflection is an isometry in which the preimage and the image have actually opposite orientations. In other words, the image appears backwards.


RotationA rotation is one isometry in i beg your pardon a number has been rotated or turned approximately a suggest called facility of rotation.



A dilation is a revolution whose preimage and image room similar. In general, a dilation is no an isometry. A dilation might be an enlargement or a reduction.


Composition that transformationA ingredient of change is a mix of 2 or an ext transformations. For example, a figure could be translated and then reflected. A figure could be reflected and also then rotated. A figure could be translated, reflected, rotated, and also dilated. That all counts on the problem and also the situation.

Looking at this number again, can you call what kind of revolutions were performed on the preimage?

The preimage was moved to the right and also we can see the the picture is smaller sized than the preimage. Therefore, the preimage was translated and dilated.

Transformations in math and the use of notation

A revolution maps a preimage ~ above its image and the symbol that we usage to describe this mapping is an arrow pointing to the right(→)

To recognize image points, we usage the element symbol ( " )

A preimage suggest could be figured out with A while the image suggest could be determined with A".

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The notation ∆ABC→∆A"B"C" means triangle alphabet maps top top triangle A element B element C prime. 

It is essential to perform the matching points that the preimage and also the picture in the same order. 

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