How to find the scale factor of a dilation?

The scale factor can be represented by the length ratio, scale factor. Or by the coordinates of a point that is not moved. It is represented by the coordinate of a point moved. Let’s know “How to find the scale factor of a dilation?” A dilation is a transformation that changes the size of an object. The scale factor of dilation is the ratio of the new size to the old size.

How to find the scale factor of a dilation?

To find the scale factor of a dilation, you need to know the new size and the old size of the object. Once you have these two pieces of information. You can divide the new size by the old size to get the scale factor.

For example, if a triangle is dilated so that its new sides are twice as long as the original sides, then the scale factor is 2.

If you only have one measurement, you can still find the scale factor. For example, if the new length of a triangle side is 6 and the old length is 3, then the scale factor is 2.

You can also find the scale factor by using proportions.

For example, if the new length of a triangle side is 6 and the old size was 3, you can set up the proportion 6/3 = x/1 and solve for x. In this case, x = 2, so the scale factor is 2.

There are also a few other ways to find the scale factor. But these are the most common methods.

No matter which method you use, the scale factor will always be the same.

Formula to find the scale factor of a dilation

The scale factor of dilation is the ratio of the lengths of the images to the lengths of the pre-images.

For example, if a line segment is dilated by a factor of 2, the new line segment will be twice as long as the original line segment.

So, the formula for the scale factor of a dilation is: n = length of new line segment/length of the original line segment.

Or, you can also say that the scale factor is the ratio of the lengths of the two line segments.

Another way to think about it is that the scale factor is the number you multiply the length of the original line segment by to get the length of the new line segment.

So, if the length of the new line segment is 2 times the length of the original line segment, then the scale factor is 2.

Read Also: How to find slope intercept form with two points?

Summary

A dilation with a scale factor greater than 1 produces an image larger than the original. And a dilation with a scale factor less than 1 produces an image smaller than the original.

The scale factor for dilation is the ratio of the lengths of the corresponding sides of the two figures. To find the scale factor, we compute the lengths of corresponding sides. In the figure, we see that the length of AC is twice the length of AB, so the scale factor is 2. We can also find the scale factor by comparing the perimeters or areas of the two figures.

Suzanna N. Alejos

I am Suzanna Alejos. I write articles for many different online publications, and manage my own blog where I share my thoughts on a variety of topics.

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