Ender, the scale factor is what we multiply by to get our new shape. Since 5 x 2 = 10, then our scale factor is 2. If we went the other way, from B to A, then it would be 1/2, because 10 x 1/2 = 5.
Or, B is twice as long as A, which means that A is half the length of B, right?
Hope this helps!
David W.
tutor
I can see your confusion. The RATIO is 1:2, also written as 1/2. If we have 5 red books and 10 black books, then the ratio of red to black is 5/10 or 1/2, but the SCALE FACTOR is still 2, since that is what we are multiplying by.
If you need to think of it as taking the reciprocal, then yes, that is what you do. A ratio of 1/3 would give us a scale factor of 3, and a ratio of 3/1 would give us a scale factor of 1/3.
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12/04/14
David W.
tutor
As I read more, I see that some places list the scale factor as the ratio of larger/smaller, so our ratio in that case would be 2/1, making our scale factor 2.
The best way to think about it is that the scale factor is what you have to multiply one by to get the other, as explained earlier. This can be figured out by taking the reciprocal of the ratio. If we had 2/3, we have to multiply 2 x 3/2 = 3, so our scale
factor is 3/2.
Confusing? Yes, but hopefully less so.
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12/04/14
Ender W.
12/04/14