Dilations

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Yesterday's homework was SCALE DRAWINGS ON iReady.

Many of you did not do the homework.

You may submit until Friday for 1/2 credit at this point.

After FRIDAY, it will remain a Zero if you do not submit it.

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TODAY: Rip out page 85-86 IT IS DUE TOMORROW BY CLASS TIME​

​Intro to Dilations

​MISSING: Please Return to Mrs. Doherty

What is a dilation ?

​Transforms a figure

Size may be enlarged, kept the same, or reduced.

​when a shape is dilated

it can ENLARGE (get larger)

or

it can ​REDUCE(get smaller)

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The image will keep the SAME shape

but NOT necessarily the same size. ​

Multiple Choice

A dilation is which of the following: 

• only an enlargement
• only a reduction
• Either an enlargement or a reduction or staying the same

• Neither an enlargement or a reduction

Multiple Choice

When A(3, 6) is under a dilation of 2 what are the coordinates of A'?

• (3, 6)

• (1.5, 3)

• (6, 12)

• (12, 6)

Multiple Choice

Which of the following is NOT true about similar figures?

• A) Similar figures always have the same shape.
• B) Similar figures always have the same size.
• C) Similar figures always have corresponding angles that are equal.
• D) Similar figures always have corresponding sides that are proportional.

Multiple Choice

If two figures are similar, the corresponding sides are ______________.

• equal
• congruent
• proportional
• none of these

Poll

what scale factor (k) best represents the dilation shown

• k=1

• k=1/2

• k=2

Open Ended

How do you know when a scale factor represents a REDUCTION?

A scale factor represents a reduction when ________________

​Multiply the lengths of the original sides by the constant (K) of 3/2 to find the new length.

​Multiply the length of each side by 1/2 to get the new length.

​Key Concepts:

• A DILATION stretches or 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

Scale Factor is represented by the letter k

• When k > 1, the shape is enlarged (gets bigger)

• When k < 1, the shape is reduced (get smaller)

• When k = 1, the shape stays the same

Multiple Choice

First, identify the old and new image. Now, did the triangle get bigger or smaller?

• The triangle got smaller

• The triangle got bigger

Multiple Choice

First, identify the old and new image. Now, did the triangle get bigger or smaller?

• The triangle got smaller

• The triangle got bigger

Multiple Choice

Is this an enlargement or a reduction?

• Enlargement

• Reduction

Multiple Choice

Is this an enlargement or a reduction?

• Enlargement

• Reduction

Multiple Choice

A dilation always produces a similar figure. Similar figures have the same ______ but different ______. 

• measure; shapes
• sizes; shapes
• value; measures
• shape; sizes

Multiple Choice

A scale factor of 1/2 reduces a figure.

• True
• False

Multiple Choice

A dilation creates a similar figure, NOT a congruent figure.

• True

• False

Multiple Choice

Dilations always result in CONGRUENT images.

• true

• false

Multiple Choice

A dilation that increases in size will always have a scale factor that is...

• negative

• exactly 1

• greater than 1

• less than 1

Multiple Choice

In this dilation, point A would be considered...

• the center of dilation

• the scale factor

• the center of rotation

• the point of no return