Notes Dilations

Definitions Dilation - a transformation in which every point P has an image P' placed on OP so that and OP' = k * OP Center of Dilation – the point from which an original figure is dilated. Scale Factor - the ratio of the image length to the corresponding original length.

Scale Factor If the scaled factor is greater than 1, then it is an enlargement (k>1). If the scaled factor is equal to 1, then it is a congruent figure (k=1) If the scale factor is less than 1, then it is a reduction (k<1).

This dilation is an enlargement . Corresponding distances Image Distance 4 2 = = 2 = k Scale Factor Original Distance 2 > 1 This dilation is an enlargement . Corresponding distances

This dilation is an reduction. Corresponding distances Image Distance 2 3 = = k Scale Factor Original Distance 2/3 < 1 This dilation is an reduction. Corresponding distances

Example: Rectangle W’X’Y’Z’ is the image of rectangle WXYZ after a dilation. Find the scale factor of the dilation. Tell whether the image is a reduction or an enlargement.

Example: 2.

Example: 3.

Reduction, Enlargement, or Congruent? K = 4 K = ½ K = 1 4>1 Enlargement ½ <1 Reduction Congruent

Matching K = ¼ K = 3 Reduction K = 2/7 Enlargement K = 1 K = 5 Congruent

7. scale factor 2

8. scale factor ¼

8. scale factor 1/3