Weeks 27/28 Transformations

Transformations

Rotation = ​Turn

Reflection =Flip

Translation = Slide

Dilation = ​Enlarge/Reduce

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tHERE ARE 4 TYPES OF trNASFORMATIONS

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Changing a shape in the coordinate plane

Shape before ​change : Preimage

Shape after change : Image​

TRANSFORMATION:

​Image

​Preimage

​Preimage

​Preimage

​Image

​Image

​TRANSFORMATION OF SHAPES CAN BE:

Translation

• Slides a figure on the coordinate plane

Sliding the shape in the coordinates plane by moving it:

Right (+) or Left (-) (on x Axis)

Up (+) or down​ (-) (on y Axis)

​All points move same distance.

TRanslations

TRanslation Rule

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In this example we can write the rule as:

translation

slide a figure
without turning it

Rotation

• turning shapes about the origin

rotation

turn a figure
about a point,
called the center
of rotation

Reflections over the y-axis

(x,y) -> (-x,y)

reflection

place point on the
opposite side of a
reflection line

Dilation

-A dilation is a transformation that produces an image that is the same shape as the original, but is a different size

-When a dilation occurs, the pre-image and image are considered to be similar but NOT congruent.

Dilation

• If a dilation creates a larger image, it is called an enlargement because it stretches the original image

• If a dilation creates a smaller image, it is called a reduction because it shrinks the original image

Dilations

• A dilation is a transformation in which a figure is enlarged or reduced with respect to a point called the center of dilation.

• With dilation, the preimage and image are similar.

• You can determine the scale factor by finding the ratio of the corresponding sides of the preimage and image.

Dilations

• To dilate a figure, with respect to the origin, multiply the coordinates of the preimage by the scale factor (k).

• If k>1, the image will be an enlargement.

• If k<1, the image will be a reduction.

• Algebraic representation: (x,y) --> (kx, ky)

​Key Concepts:

• A DILATION stretches of shrinks a figure.

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• The CENTER OF DILATION never changes position. It is the starting point.

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• ​The SCALE FACTOR tells you how much the dilation stretches or shrinks.

A DILATION is a transformation that produces an image that is the same shape as the pre-image, but is a different size. Dilations create similar figures. 

• Scale factor is greater than 1​

• Image gets BIGGER​

Enlargement

• Scale factor is less than 1​

• ​Image gets SMALLER

​​Reduction

The Scale Factor

• We use the scale factor(sf) to help describe and determine the type of dilation that takes place

• If sf > 1; the dilation is an enlargement

• is sf < 1; the dilation is a reduction

• if sf = 1; the image and pre-image are the exact same

Real Life Examples of Dilations

Real Life Examples of Dilations

Real Life Examples of Dilations

Multiple Choice

What are the coordinates for C' after a reflection over the y-axis?

• (1,2)

• (-1,-2)

• (2,1)

• (-1,2)

Multiple Choice

Triangle EFG will be rotated 90 degrees counterclockwise about the origin. What will be the coordinates of E'?

• (-2,-1)

• (-1,-2)

• (1,-2)

• (2,1)

Multiple Choice

Identify the transformation from A to D.

• 90^o Clockwise Rotation

• 180^o Rotation

• 270^o Clockwise Rotation

• 360^o Rotation

Multiple Choice

Point (-3,-3) is rotated 360 degrees clockwise about the origin.  Where is the new point located?

• (3,3)

• (-3,3)

• (3,-3)

• (-3,-3)

Multiple Choice

The Transformation in this picture is

• Rigid

• Non Rigid

Multiple Choice

Which of the following transformations is rigid?

Multiple Choice

Is the following transformation rigid or non-rigid?

• Rigid

• Non Rigid

• We can't tell!

Multiple Choice

Which of the 4 types of transformations is non-rigid transformation?

• Rotation

• Reflection

• Translation

• Dilation

Multiple Choice

What are the coordinates of B' after a reflection over the x-axis?

• (-2,4)

• (4,-2)

• (-2,-4)

• (2,4)