13.5 Dilation

13.5 Dilation

Dilations

• Dilations is our last of our transformations.

• We've looked at translating them (slide), reflecting them, and rotating them.

• Dilations refer to proportionally changing the size of the same shape (small to large, large to small)

• The blue image is a dilation of the black image.

• Would we say the blue image is an enlargement or reduction of the black image?

• Enlargement - the blue image grew in size compared to the black one.

• Next we would need to find the scale factor; how much larger is the blue compared to the black one

• Because the blue shape is the image (and the black is the pre-image), we know that our ratio will be  $\frac{15}{9}\rightarrow\ \frac{5}{3}$  

Fill in the Blanks

The blue shape is a reduction of the black shape. What is the scale factor? (hint: you only need to compare one side of each shape!)

Reasoning for the previous question:

• Because the blue shape is a reduction of the black one, then our scale factor's numerator is going to be smaller than our denominator.

• One side of the blue shape is 2 units, and one side of the black is 4 units, so it will be 2/4, or 1/2 simplified.

Scale factor

• "Find the images of the vertices of Δ​PQR, shown​ below, for a dilation with center​ (0,0) and scale factor 2. Then graph the image

• Our black shape is our original triangle. We need to find the points to a enlarged triangle with a scale factor of 2.

• If you notice in the top left, we need to find each of our original points (of the black one), and because we have a scale factor of 2, multiply each point by 2, like I've done. Then the red triangle is the enlarged image with a scale factor of 2.

Fill in the Blanks

Notice the scale factor. If PQ is 7, what would be P'Q'?

Reasoning for previous question

• Notice the scale from from NP to N'P' is 5 (4x?=20)

• Then PQ to P'Q' is 35.