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What does scale factor look like?

These pictures were taken from the website http://www.regentsprep.org/Regents/math/geometry/GT3/Ldilate.htm and demonstrate that a scale factor makes a copy of an image that can be larger or smaller than the original image, like a copying machine.
Dtigers.gif

washers.gif






What is scale factor?




Scale Factor includes a lot of concepts. It always involves similar figures, and it includes concepts about rates. To put it simply, corresponding (matching) sides have the same ratio this ratio is called the scale factor. It doesn't matter what shape you have, as long as you have similar figures you should be able to find the scale factor and use it. To determine what the scale factor is, you just have to remember NO. NO means you put the corresponding sides in a ratio with the New side overOld side. The new side always has a prime. You also should be able to form a proportion from the matching sides of similar figures. This proportion allows you to find the value of a missing side. These are only a few examples of how to apply the concept of scale factor. There are more ideas within this concept, but if you can remember these things it can really help to apply scale factors.


These words are associated with scale factors :

Dilation
Enlargement
Reduction

You will expand your vocabulary with respect to these words in high school

If the scale factor is less than one it means that we have a reduction. However, if the scale factor is more than one it means that we have an enlargement.

We know that this is true because 100% is the same as 1 whole.
Similarly:










To understand how this works think about what happens when you use a copying machine. The machine uses scale factors to figure out if you want to copy exactly as it is (100%), make it smaller (less than 100%), enlarge it (more than 100%).


Think about it

If you put 50% as your scale factor in the machine, what happens?



answer: you make a copy where everything looks half as big.


If you put 200% as your scale factor in the machine, what happens?


answer: you make a copy where everything looks twice as big.


DiPic.gif





Scale_factor_1.jpg
As we said before the new figure is A' B' C' D'. We know that this is the new figure because the new figure always has " ' " or "prime" on each of its points.

Remember that we can use NO to find the scale factor. It doesn't matter which corresponding sides we pick to apply NO. Let's pick sides AD and A'D' since they match. The New side over Old side formula looks like:




Since



The scale factor is 1.5.

In the above example the two figures were drawn separately. Sometimes the figure's dilation is drawn along with the original figure. For example:

Notice that if we multiply a side by the scale factor we get the corresponding side:

In other words the old side (AD) times the new side (A'D') gives you the scale factor.



or when we put the values of AD and A'D' in we get



This is important to know because it makes certain scale factor questions easier. For example if you are given the length of one side and the scale factor and you are asked to find the length of the matching side on the new figure you should multiply.

Example:
A circle with a radius of 3 inches was reduced using a scale factor of 0.4. What is the length of the radius of its image?








Multiplying by the scale factor can also happen on a graph. The trick is to see that although the dilated figure is shown with the original figure, they are actually two separate figures.


For example:
Scale_factor_2.jpg

Student explanation of scale factor:















More examples of scale


Missouri City Middle School Eighth Grade Math Class

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