how to find the scale factor of a dilation

Enter the change in x and change in y of a length along with a shape or image pre and post-scaling to calculator the scale factor dilation.

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Scale Factor Dilation Formula

The following formula is used to calculate the scale factor dilation of an image or shape.

SF = X2/X1 = Y2/Y1

Where SF is the scale factor dilation
X2 and Y2 are the change in X and Y of the final image
X1 and Y1 are the change in X and Y of the original image

Scale Factor Dilation Definition

A scale factor dilation is a ratio of the length or area of an image before and after it has been enlarged or shrunk.

Scale Factor Dilation Example

How to calculate a scale factor dilation?

First, determine the change in X and Y of the original image.
Measure the change in X and Y of a single length of the original image.
Next, determine the change in X and Y of the modified image.
Measure the change in X and Y of the same length on the modified image.
Finally, calculate the scale factor dilation.
Calculate the total scale factor dilation using the equation above.

Example Problem:

The following is a step-by-step example problem for calculating a scale factor dilation. This example follows the how-to calculate instructions from directly above.

First, the change in x and y of the original image must be determined. Measuring these two values we find these to be 5 and 7 respectively.

Next, the change in x and y of the modified image must be measured. For this example, these are found to be 10 and 14 respectively.

Finally, we can calculate the scale factor dilation using the formula above:

SF = X2/X1 = Y2/Y1

SF = 10/5 = 14/7

SF = 2 = 2

FAQ

What is scale factor dilation?

A scale factor dilation is a rate at which an image or shape is enlarged or shrunk to produce a scaled version of the image.