dilation


Definition of Dilation

  • Dilation is a similarity transformation in which a figure is enlarged or reduced using a scale factor ≠ 0, without altering the center.

Examples of Dilation

  • In the figure shown, triangle ADE is enlarged to triangle ABC using a scale factor 4. Here, A is the center of dilation.

More about Dilation

  • When the scale factor of a dilation is greater than 1, the dilation is an enlargement.
  • When the scale factor of a dilation is less than 1, the dilation is a reduction.

Solved Example on Dilation

A'B'C'D' is a dilation of ABCD. Find the scale factor if AB = 2 × A'B'.
Choices:
A. 2
B. 5
C. 0.5
D. 0.2
Correct Answer: C
Solution:
Step 1: A'B'C'D' is a dilation of ABCD.
Step 2: AB = 2 × A'B' implies A'B' = 0.5 × AB
Step 3: So, the scale factor is 0.5.

Related Terms for Dilation

  • Similarity Transformation
  • Enlargement
  • Reduction
  • Scale Factor
  • Center