Dilations or scaling around a point

4 videos
4 skills
In addition to the three rigid transformation, there are the dilations, which expand or shrink figures while keeping the same proportions. These are extremely important in the subject of Similarity! Gain experience by performing dilation, learn how to find the dilation that maps a given figure to another, and learn how to manually draw the image of a dilation.

How to perform a dilation (example)

VIDEO 2:46 minutes
Sal shows how to perform a dilation on a hexagon using our interactive widget!

Perform dilations

PRACTICE PROBLEMS
Use the interactive transformation tool to perform dilations.

How to map a given line into another using a dilation (example)

VIDEO 3:59 minutes
Sal shows how we can use dilations to map a line into another, parallel, line.

Find the dilation that maps a given figure to another (basic)

PRACTICE PROBLEMS
Either find the scale factor or the center of a dilation that maps a given figure into another. Map a line into a different parallel line using dilations.

Find the dilation that maps one figure to another (advanced)

PRACTICE PROBLEMS
Find both the center and the scale factor of a dilation that maps a given figure to another one.

How to draw the image of a shrinking dilation about the origin (example)

VIDEO 2:26 minutes
Sal is given a triangle on the coordinate plane and he draws the image of the triangle under a dilation with scale factor 1/2 about the origin.

How to draw the image of an expanding dilation about an arbitrary point (example)

VIDEO 2:39 minutes
Sal is given a rectangle on the coordinate plane and he draws the image of the rectangle under a dilation with scale factor 1 2/3 about an arbitrary point.

Draw the image of a dilation

PRACTICE PROBLEMS
Given a figure and a definition of a dilation, manually draw the image.