Verify experimentally the properties of dilations given by a center and a scale factor. A dilation takes a line not passing through the center of the dilation to a parallel line and leaves a line passing through the center unchanged. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Sample Practice Questions (3)

In the diagram below,

△ A^{'} B^{'} C^{'}

is the image of

△ A B C

after a dilation centered at the origin. What is the scale factor of the dilation?

k = 3

k = \frac{1}{3}

k = 2

k = 9

In the coordinate plane, segment

A B

has endpoints

A (1, 1)

and

B (2, 2)

. If

A B

is dilated by a scale factor of

k = 3

centered at the origin to create segment

A^{'} B^{'}

, what are the coordinates of

B^{'}

(6, 6)

(5, 5)

(3, 3)

(2, 6)

In the coordinate plane shown, segment

A^{'} B^{'}

is the image of segment

A B

after a dilation centered at the origin. What is the scale factor of this dilation?

k = 3

k = \frac{1}{3}

k = 2

k = 1.5

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