Dilations Lesson

Dilations Lesson

Pre-Algebra

Mrs. Austin

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)

Multiple Choice

Triangle ABC will be dilated by a scale factor of 1/2.  What will be the coordinates of C'?

• (-1, -2.5)
• (12, 6)
• (3, -1.5)
• (0, 1.5)

Multiple Choice

Dilate Point B by a scale factor of 1/2

• (1.5,-4)
• (-1.5,1)
• (-1,-1.5)
• (-2,-2)

Multiple Choice

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?
A(3,3) B(6,6) C(9,3)

• A'(9,9) B'(18,18) C'(27,9)
• A'(6,6) B'(9,9) C'(12,6)
• A'(0,0) B'(3,3) C'(6,0)
• A'(1,1) B'(2,2) C'(3,1)

Multiple Choice

Does the image show a Dilation? If yes, did the image enlarge, reduce or none of the above?

• Yes, enlarge
• Yes, reduce
• No

Multiple Choice

Did the image enlarge, reduce or none of the above?

• Enlarge
• Reduce
• None of the above

Multiple Choice

If your SF = 0.8, what type of dilation is it?

• Reduction

• Enlargement

Multiple Choice

If your SF = 2.5, what type of dilation is it?

• 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

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

• addition 
• subtraction 
• multiplication 
• division 

Multiple Choice

When the scale factor of a dilation is less than one, the dilation is a reduction.

• True
• False

Multiple Choice

When a dilation has a scale factor greater than one, the dilation is an enlargement.

• True
• False

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