Dilation Explorer

Extend your learning by exploring scale factors, dilations about the origin, and how dilations affect perimeter and area.

Watch the related lessons to review dilations from different centers, fractional scale factors, and how figures stretch or shrink.

Use the Dilation Explorer to investigate how a figure changes size from a center of dilation.

Drag the pre-image or move individual vertices to create your own figure. You can also drag the center of dilation to a new location.

Use the scale factor slider to reduce, enlarge, or keep the figure the same size while comparing the original coordinates to the image coordinates.

What happens when the scale factor is less than \(1\)?

What happens when the scale factor is greater than \(1\)?

How does changing the center of dilation affect the location of the image?

Transformation: A change in the position, size, or orientation of a figure.

Dilation: A transformation that changes the size of a figure from a center point.

Scale Factor: The number used to multiply distances from the center of dilation.

Reduction: A dilation with a scale factor between \(0\) and \(1\), which makes the image smaller.

Enlargement: A dilation with a scale factor greater than \(1\), which makes the image larger.

Same Size: When the scale factor is exactly \(1\), the image is the same size as the pre-image.

Center of Dilation: The fixed point from which the figure is enlarged or reduced.

Pre-image: The original figure before a transformation.

Image: The new figure after a transformation.

Similar Figures: Figures that have the same shape but not necessarily the same size.

Congruent: Figures that have the same size and shape. A scale factor of \(1\) creates a congruent image.

Non-rigid Transformation: A transformation that does not always preserve size.

A dilation changes the size of a figure by multiplying distances from the center of dilation by the scale factor \(k\).

When the center of dilation is the origin, the coordinate rule is:

\((x,y) \rightarrow (kx,ky)\)

If \(0 < k < 1\), the image is a reduction. If \(k = 1\), the image is the same size. If \(k > 1\), the image is an enlargement.

For example, a dilation with scale factor \(2\) centered at the origin can be written as \((x,y) \rightarrow (2x,2y)\).

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