Intro to Dilations

​Introductions to Dilations

​Welcome back from Winter Break

Fill in the Blank

When Juno was 8 years old, her brother Luke was half her age. If Juno is 30 years old today, how old is Luke?

Dilation

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

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

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Dilation changes the position and size of a figure but not the shape.

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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

Labelling

Label the diagram and fill in your notes on your sheet.

Drag labels to their correct position on the image

be distorted

reduction

stays the same

enlargement

scale factor

change in size

Multiple Choice

Triangle ABC is dilated by a scale factor of 8 to form Triangle A’B’C’ with the origin as a center of dilation. Which rule represents this dilation? 

• $$(8x,8y)\ \rightarrow\ (x,y)\$$  

• $$(x,y)\ \ \rightarrow\ \ (x+8,\ y-8​)$$  

• $$(x,y)\ \rightarrow\ (8x,\ 8y)$$  

• $$(x,y)\ \ \rightarrow\ \ (\frac{x}{8},\ \frac{y}{8})$$  

Multiple Select

Which of the following algebraic rules represents an enlargement?
Select all that apply

***There's more than 1 correct answer!

• $$(x,y)\ \rightarrow\ (1.6x,1.6y)$$  

• $$(x,y)\ \rightarrow\ (0.75x,0.75y)$$  

• $$(x,y)\ \rightarrow\ (\frac{18}{5}\ x,\ \frac{18}{5}\ y)$$  

• $$(x,y)\ \rightarrow\ (-x,y)$$  

Multiple Select

Which of the following algebraic rules represents a reduction?
Select all that apply

***There's more than 1 correct answer!

• $$(x,y)\ \rightarrow\ (3x,3y)$$  

• $$(x,y)\ \rightarrow\ (\frac{3}{4}x,\ \frac{3}{4}​y\ )$$  

• $$(x,y)\ \rightarrow\ (0.99x,0.99y)$$  

• $$(x,y)\ \rightarrow\ (5x,\ 5y)$$  

Real Life Examples of Dilations

Real Life Examples of Dilations

Real Life Examples of Dilations

​Find the scale factor used to create the scale factor

​Scale Factor = new divided by the old.

​​​First identify the corresponding/ similar sides in the figures.

• ​ EX: Side GH which is 8cm corresponds to side G'H' which is 10 cm.

​Take any of the matching sides and divide the new measure by the old measure.

• ​Notice how the new image is larger than the pre-image. This is because the Scale factor is greater than 1.

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Multiple Choice

Which rule best represents the dilation that was applied to Pentagon EFGHI to create Pentagon E'F'G'H'I’?

• $$(x,y)\rightarrow\ (x+2,y-4)$$

• $$(x,y)\ \rightarrow\ (0.33x,0.33y)$$

• $$(x,y)\ \rightarrow\ (3x,3y)$$

• $$(x,y)\ \rightarrow\ (x-2,y+4)$$

Multiple Choice

Trapezoid ABCD was dilated with the origin as the center to create Trapezoid A'B'C'D’.

Which rule best represents the dilation that was applied to Trapezoid ABCD to create Trapezoid A'B'C'D' ?

• $$(x,y)\ \ \rightarrow\ \ (\frac{1}{2}x,\frac{1}{2}​y)$$

• $$(x,y)\ \ \rightarrow\ \ (2x,\ 2y)$$

• $$(x,y)\ \ \rightarrow\ \ (4x,\ 2​y)$$

• $$(x,y)\ \ \rightarrow\ \ (-x,\ -y)$$

Multiple Choice

Which rule best represents the dilation that was applied to quadrilateral WXYZ to create quadrilateral W’X’Y’Z’?

• $$(x,y)\rightarrow\ (\frac{4}{10}​x,\ \frac{4}{10}​y)$$

• $$(x,y)\ \rightarrow\ (x+3,y+2)$$

• $$(x,y)\rightarrow\ (\frac{10}{4}​x,\ \frac{10}{4}​y$$

• $$(x,y)\ \rightarrow\ (x-3,y-2)$$

Fill in the Blank

Scale Factor:_____ (enter number only

Multiple Choice

Find the coordinates of the vertices of the figure after the given transformation.

• A

• B

• C

• D

Multiple Choice

Find the coordinates of the vertices of the figure after the given transformation.

• A

• B

• C

• D

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Complete the remainder of your assignment on pages 1-3

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