Making scaled copies

• [Instructor] Figure A is a scaled copy of figure B. And then they say what is the value of x? Pause this video and see if you can figure that out.

All right, given that figure A is a scaled copy of figure B, that would also mean that figure B is a scaled copy of figure A. And so we would have a common scale factor between corresponding sides.

So, for example, this side right over here, it looks like it's playing the same role as this side right over here. And so what would be the scale factor to go from 10 to 12.5? What do I have to multiply 10 by to get 12.5?

Well, I'm multiplying it by a scale factor. I'm using a scale factor of 1.25. I'm multiplying times 1.25, or you could also think of it as I'm multiplying times 1 1/4, either way of expressing the same number.

Well, if I'm thinking about x, if I want to know this length right over here, corresponding to this side on figure B would be this side on figure A, which has length 16. And so I would use the same scale factor.

So my scale factor here, once again, would be 1 1/4. So I'll multiply times 1 1/4. And 1/4 of 16 is four. So it's going to be 16 and then another four is going to be equal to 20.

1.25 times 16 is equal to 20, and we're done.

Let's do another example. Here we're told figure A is a scaled copy of figure B. All right. Figure A is made from figure B using a scale factor of 5/2. What is the value of x? Pause this video and see if you can figure that out.

Well, when they tell us that figure A is made from figure B using a scale factor of 5/2, that means when we're making figure A, if we look at the corresponding side on figure B, so we have this side on figure B.

It looks like it corresponds to this side on figure A. And so to go from five to x, we would use a scale factor of 5/2. We're gonna multiply by 5/2.

Well, what is five times 5/2? Let me just write here, x is going to be equal to five times our scale factor, times 5/2, which is going to be equal to 25.

Let me write it this way. It's going to be equal to 25 over two, which, if we want, we could write it as 12.5. So x right over here, the length right over here, is 12.5.