Congruence & Similarity Worksheet: Dilations

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1. The original coordinates of a figure are (1,2); (-3,2); (8,0); (0,-8).

What are the new coordinates of a figure after S4?

   (4,8); (-12,8); (32,0); (0,-32)   

2. The original coordinates of a figure are (1,2); (-3,2); (8,0); (0,-8). After a size transformation, the new coordinates are (5,10); (-15,10); (40,0); (0,-40). What was the factor of the size transformation?


3. Triangle XYZ is shown on the Cartesian plane. Draw a similar triangle with a size transformation of 2.

   (-4,0); (4,0); (8,0)   

Click here to see triangle


cartesian grid with triangle plotted

4. Draw a 4 x 4 square at the center of the Cartesian plane. Then perform a transformation of S1.5. Using the new coordinates, draw a second square on the Cartesian plane.

 The coordinates of the smaller square
(2,-2); (-2,2); (2,2); (-2,-2)

Multiply each of those numbers by 1.5.
The new coordinates
(3,-3); (-3,3); (3,3); (-3,-3)    

Click here to see triangle

blank cartesian grid

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Related Resources

The various resources listed below are aligned to the same standard, (8G03) taken from the CCSM (Common Core Standards For Mathematics) as the Geometry Worksheet shown above.

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.


Similarity, Congruence and Transformations


Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Understand congruence and similarity using physical models, transparencies, or geometry software