TRANSFORMATIONSTRANSFORMATIONS

SPI 3108.3.3SPI 3108.3.3

SPI 3108.4.10SPI 3108.4.10

TYPES OF TYPES OF TRANSFORMATIONSTRANSFORMATIONS

ReflectionsReflections – The flip of a figure over – The flip of a figure over a line to produce a mirror image.a line to produce a mirror image.

RotationRotation – A geometric turn of a – A geometric turn of a figure around a fixed point.figure around a fixed point.

TranslationTranslation – The slide of a figure – The slide of a figure from one position to another.from one position to another.

DilationDilation – A transformation that alters – A transformation that alters the size of a figure, but not its shape.the size of a figure, but not its shape.

Preimage to ImagePreimage to Image

A

B

C

D

Each point on the original figure is called the Preimage

B’

A’ C’

D’ Its matching point on the corresponding figure is called its image.

ReflectionsReflections

REFLECTIONREFLECTION – The flip of a figure over – The flip of a figure over a line to produce a mirror image.a line to produce a mirror image.

Coordinate Reflection Coordinate Reflection

The triangle is reflected about the x-axis. Each point is equal distance from the x-axis.

RotationRotation

The triangle PAD is rotated 90 degrees counter clockwise about the point P. To accomplish this the segment PD is used as the base line. Segment PD is rotated until it forms a 90 degree angle. The remainder of the triangle is formed from segment PD.

D

D’

A

A’

P

900

ROTATIONROTATION – A geometric turn of a figure – A geometric turn of a figure around a fixed point.around a fixed point.

TranslationTranslation

Slide

TRANSLATION– The slide of a figure from one TRANSLATION– The slide of a figure from one position to another.position to another.

Coordinate TranslationCoordinate Translation

Each point is translated 3 points to the right and 5 points up.

DilationDilation

Dilation is altering the size of the figure by k = n . The dilation of this figure is k = 3. The image is 3 times bigger than the preimage.

DILATION – A transformation that alters the size of DILATION – A transformation that alters the size of a figure, but not its shape.a figure, but not its shape.

Coordinate DilationCoordinate Dilation

Each point is multiplied by k to find the dilation.