Dilations

Graphing

Graph the triangle ABC: A(2,2), B(2,4), C(4,2) and then dilate the figure by a scale factor of 1/2.

Graphing

Graph the trapezoid ABCD:: A(2,2), B(3,4), C(5,4), D(5,2) and then dilate the figure using a scale factor of 2.

Graphing

Graph the rectangle PQRS: P(-2,2), Q(0,2), R(0,-2), S(-2,-2) and then dilate the figure using the scale factor of 3.

Graphing

Dilate the following triangle by a scale factor of 1/4.

A (-4, -4), B (4, 4) C (4, 0)

Open Ended

What happens when you apply a scale factor greater than 1 to a set of coordinates?

Open Ended

What happens when you apply a scale factor less than 1 to a set of coordinates?

Multiple Choice

What is Dilation?

• Dilation means to enlarge or reduce
• Dilation means to reflect on something
• Dilation means to like something
• Dilation means to make something different by making it smaller

Multiple Choice

The __________ is the ratio of a length of the image to the corresponding length on the original figure.

• reduction
• enlargement
• scale factor
• center of dilation

Multiple Choice

A scale factor of less than one means

• that the prime image will be larger than the pre-image.
• That the prime image will be the same as the preimage.
• That you need to subtract that amount off  of each side.
• That the prime image will be a reduction of the preimage.

Multiple Choice

Choose the correct scale factor:

• 2
• 3
• 1/3
• 1/2

Multiple Choice

Dilate Point B by a scale factor of 3:

• (12,0)
• (12,12)
• (4,3)
• (0,12)

Multiple Choice

Choose the correct scale factor:

• 2
• 3
• 1/3
• 1/2

Multiple Choice

State the coordinate of the image of the given point B (-10,-6) under a dilation with the scale factor of 1/2.

• (5,3)

• (20,12)

• (-20,-12)

• (-5,-3)

Multiple Choice

Dilate Point A by a scale factor of 1/2

• (-4,-4)
• (-1,-4)
• (-1,-1)
• (-2,-2)

Multiple Choice

How do you write the algebraic notation when the scale factor is 3?

• (x, y) goes to (1/3x, 1/3y)
• (x, y) goes to (-3x, -3y)
• (x, y) goes to (x + 3, y + 3)
• (x, y) goes to (3x, 3y)

Multiple Choice

The red triangle has been dilated by a scale factor of 1/4, which triangle is it's new image? 

• green triangle 
• red triangle 
• black triangle
• none of these 

Multiple Choice

What is the rule for the dilation pictured below?

• (x, y) → (½x, ½y)
• (x, y) → (x + 2, y + 2)
• (x, y) → (2x , 2y)
• (x, y) → (2x, 3y)

Multiple Choice

A __________________ is a transformation that enlarges or reduces the size from pre-image to image based on a scale factor.

• translation

• reflection

• rotation

• dilation

Multiple Choice

An ________________means that the image is larger than the pre-image.

• reduction

• enlargement

• flip

• spin

Multiple Choice

A dilation is which of the following: 

• only an enlargement
• only a reduction
• Either an enlargement or a reduction
• Neither an enlargement or a reduction

Multiple Choice

In a dilation what mathematical operation is used with the scale factor?

• addition 
• subtraction 
• multiplication 
• division 

Multiple Choice

A ________________means that the image is smaller than the pre-image.

• flip

• spin

• reduction

• enlargement

Multiple Choice

The __________ is the ratio of a length of the new figure to the corresponding length on the original figure.

• reduction
• enlargement
• scale factor
• center of dilation

Multiple Choice

When the scale factor is greater than 1 on a dilation, it produces ___________________.

• a reduction

• a pre-image

• a spin

• an enlargement

Multiple Choice

What scale factor was used to produce the image?

• 2
• -2
• ¹/₂
• 1

Multiple Choice

When dilations have a scale factor of less than 1, it causes a ___________________.

• reduction

• enlargement

• slide

• turn

Multiple Choice

Enlargement or reduction?  Find the scale factor!

• It's an enlargement; the scale factor is 1/2.
• It's an enlargement; the scale factor is 2.
• It's a reduction; the scale factor is 1/2.
• It's a reduction; the scale factor is 2.

Multiple Choice

Which scale factor will cause a reduction

• 4

• 100

• 7

• 1/4

Multiple Choice

Sides that are in the same position are called

• Corresponding Sides
• Corresponding Angles
• The Same
• Congruent Sides

Multiple Choice

Which scale factor will cause an enlargement?

• 5

• 0.5

• 5/10

• 0.55

Multiple Choice

If the scale factor is less than one, the new figure will be

• an enlargement
• a reduction
• a scale factor
• bigger

Multiple Choice

Similar figures are figures that are the SAME shape, but a DIFFERENT size.

Which one of the following transformations will produce a similar figure?

• translation

• dilation

• rotation

• reflection

Multiple Choice

If the scale factor is greater than one, the new figure will be

• a reduction
• an enlargement
• a scale
• not proportional

Multiple Choice

Congruent figures are figures that are the SAME size and the SAME shape.

All of these transformations produce congruent figures EXCEPT which one?

• translations

• reflections

• rotations

• dilations

Multiple Choice

The point A (8, 12) was dilated to become point A' (2, 3). What was the scale factor?

• ½

• ¼

• 4

• 2

Multiple Choice

A dilation with a scale factor of 4 will produce an enlargement.

• true

• false

Multiple Choice

What is the scale factor?

• 1/2

• 2

• 4

• None of the above

Multiple Choice

A dilation with a scale factor of 2 will produce a reduction.

• true

• false

Multiple Choice

Dilations result in a similar shape (same shape, different size).

• True

• False

Multiple Choice

A dilation with a scale factor of 1/3 will produce a reduction.

• true

• false

Multiple Choice

The blue triangle is the pre-image (original shape). The red shape is a ________________ of the blue shape.

• enlargement

• reduction

Multiple Choice

In this dilation, the blue figure is the image and the black figure is the pre-image. This means that an ______________ occurred.

• enlargement

• reduction

• spin

• flip

Multiple Choice

Is the image an enlargement or reduction of the original shape?

• enlargement

• reduction

Multiple Choice

In this example of a reduction, the blue figure is the image which means the scale factor has to be __________________.

• more than 1

• equal to 1

• less than 1

• nothing

Multiple Choice

State the coordinate of the image of the given point B (-10,-6) under a dilation with center at the origin with the given scale factor k = 1/2.

• (5,3)
• (20,12)
• (-20,-12)
• (-5,-3)

Multiple Choice

When trying to find the side lengths of the image or the coordinates of the image in a dilation, what operation do you perform using the scale factor?

For example: A (2,1) and the scale factor is 3, A' will be (6,3).

• add

• subtract

• multiply

• divide