1.14 Dilations

Manipulate the figure above by changing k and by changing it center. This transformation is called a dilation.

k is called the scale factor. What happens to the figure when "k" is negative? What happens when "k" is less than 1? What happens when "k" is greater than 1? What happens to the figures when the center is inside, on, or outside one of the figures?

Use the line tools to find the center of this dilation.

Click all of the boxes above. Move the slider so that the "scale" changes.

What do you notice about the sides? Give an example.

Use the figure below to answer these questions.

1. If the dilation is an expansion, what will the values of k (scale factor) be?[br]2. If the dilation is a contraction, what will the values of k be?[br]3. What happens when k is negative?[br]4. What happens when k = 1?

Using Algebra rule for dilations (center must be at the origin). Find A'B'C'. What is the scale factor?

Rule: (x,y)------->(3x,3y)[br]A( 2,1)[br]B( -3,2)[br]C(0,4)

Draw the dilation (preimage and image) using the algebra rule above.

Using Algebra rule below for dilations (center must be at the origin). Find A'B'C'. What is the scale factor?

Rule: (x,y)------->(2x,2y)[br]A( 2,1)[br]B( -3,2)[br]C(0,4)

Use the dilation tool to draw the transformation on the graph below.[br]Rule: (x,y)------->(2x,2y)[br]A( 2,1)[br]B( -3,2)[br]C(0,4)

Use the dilation tool to draw the transformation on the graph below.[br]Rule: (x,y)------->(0.5x,0.5y)[br]A( 2,1)[br]B( -3,2)[br]C(0,4)

What do you think? Does the function rule work if the center of the dilation is not at the origin?