Reciprocal scale factors
In the second example the narrator asks 'what do I have to multiply to go from 1 to 1/2?' when the side actually goes from 2 to 1/2; the answer 1/4 is still correct.
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If figure B is a scaled copy of figure A with scale factor k, then going back from B to A uses the reciprocal, 1/k. The video finds scale factors of 2 and 1/2 in one example, and 1/4 and 4 in another.
You'll be able to
- find the scale factor from one figure to another using corresponding sides.
- explain why the scale factor in the opposite direction is the reciprocal.
- find the reciprocal of a whole number or a unit fraction.
Key words
- scale factor
- The number you multiply a side of one figure by to get the matching side of the other.
- reciprocal
- The number you multiply by to get 1, such as 1/2 for 2, or 4 for 1/4.
- scaled copy
- A figure whose sides are all the original sides multiplied by the same number.
Transcript
- [Instructor] We're told that figures A and B are scale copies, and the first thing I'm gonna ask you is, what is the scale factor? Scale factor from figure A to figure B. Pause this video and try to figure that out. Well, let's look at two corresponding sides.
So, if we look at the bottom side of these triangle, which look like they're corresponding, we can see that figure A has a length of 4, and figure B has a length of two, four, six, eight, so we are multiplying corresponding sides by 2 to go from figure A to figure B.
We could do that with the other sides as well. So, the scale factor for figure A to figure B is 2. Now, what if we were to do it the other way around? What would be the scale factor, scale factor from figure B, figure B, to figure A? Well, if we multiply by 2 to get to figure B, a corresponding side.
If I'm starting with figure B and I wanna get to figure A, I would multiply by the reciprocal of 2. I would multiply by 1/2. I would take this 8 and multiply by 1/2 to get to that 4. So, this is going to be equal to 1/2, the reciprocal of 2. Let's do another example.
Here, once again, we're told that these two are indeed scale copies, and let's figure out the scale factor, I just won't write it out, scale factor of figure A to figure B. So, same exercise. Pause this video, try to figure that out. Okay, so if we look at corresponding sides here, I'll go from this left-hand side, we're going from 2 to 1/2.
So, what do I have to multiply to go from 1 to 1/2? 1/2 is 1/4 of 2. I have to multiply by 1/4. and we could see that with the other sides. If I multiply this by 1/4, I get to 1/2. If I multiply 3 by 1/4, I get to 3/4. So, the scale factor is 1/4. Now, what if we were to do it the other way around?
What is the scale factor from figure B to figure A? Well, as we just saw, it's gonna be the reciprocal of that. If we multiply by 1/4 to go from A to B, we're going to multiply by 4 to go from B to A. So, this is going to be 4, the reciprocal of 1/4. They are the reciprocals of each other.
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