8th Grade - Dilation


  • To transform a figure (shape) means changing the size, location, and direction it faces.
  • The figure before the transformation is called the pre-image
  • The figure after the transformation is called the image
  • If the pre-image is labeled as A, then the image would be labeled as A' (pronounced as A prime).
  • There are four different types of transformation.
    1. Dilation
    2. Reflection
    3. Rotation
    4. Translation


  • The image after the dilation is similar to the pre-image.
  • Two images are similar if:
    • They are of different sizes with proportional sides.
    • All angles are congruent.
    • They can be mapped on one another with a series of transformations.
  • The symbol for similarity is ∼.



  • A dilation is a type of transformation that resizes (stretches or shrinks) the original figure.
  • A dilation produces an image that is the same shape as the original but different in size.
  • Dilation produces similar but not congruent images.
  • It enlarges or reduces the size of the original figure (pre-image) with a scale factor
  • A dilation needs a center point, also called as the center of dilation, and a scale factor.
  • The center of dilation or the center point is a fixed point in the plane. 
  • The scale factor is a ratio of the corresponding sides in a figure.                   
  • A scale factor between 0 and 1 means the resulting image will be shrunk/reduced.
  • A scale factor > 0 means the resulting image will be enlarged.
  • A scale factor of 1 means the pre-image and image are congruent. 


Solved Examples

Question 1: If the scale factor of a dilation centered at the origin is 3, find the image of the point (2, 7).

Solution: If the scale factor is k=3, it follows the dilation rule x,y3x, 3y.

Hence, the dilated image of the point (2, 7) will be 3×2, 3×76, 21.

Question 2: ABC is plotted on the coordinate grid. If the figure were dilated by a scale factor 52 with the origin as the center of dilation, what are the coordinates of the vertices of A'B'C'.


Pre-image Image after dilation  scale factor=52
A-4, 8 A'-10, 20
B8, 6 B'20, 15
C4, -2 C'10, -5


Question 3: A'B'C' is the image of ABC under a dilation with a scale factor of 4 as shown in the figure below. Find the length of segment A'C'¯.

Solution: scale factor=corresponding side length of imagecorresponding side length of pre-image

scale factor=A'C'AC


A'C'=4×4=16 units

Cheat Sheet

  • Look for keywords: Stretch, Enlarge, Reduce, and Shrink.
  • In dilation, the figure stretches or shrinks based on a scale factor.
  • x,y kx,ky where k is the scale factor.
  • Dilated images are similar but not congruent.

Blunder Areas

  • Differentiate between pre-image (A) and image (A').
  • The scale factor in fractions does not always reduce the size of the figure.