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.
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
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.
