Corresponding distances in scaled figures
The narrator's mental arithmetic for 6 x 18.5 is garbled ('60 plus 40, 808'), but he then redoes it on paper and correctly gets 111/10 = 11.1.
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Because figure A is a scaled copy of figure B, the ratio of any distance to a side in one figure equals the matching ratio in the other. The video sets up the proportion 18.5/10 = x/6 and solves it to get x = 11.1.
You'll be able to
- set up a proportion using corresponding distances in scaled copies.
- solve a proportion to find a missing distance.
- recognise that there is more than one correct way to set up the proportion.
Key words
- scaled copy
- A figure where every distance in the original is multiplied by the same number.
- ratio
- A comparison of two amounts, like 18.5 to 10.
- corresponding sides
- Sides or distances in matching positions in two figures.
Transcript
- [Instructor] So, we're told Figure A is a scale copy of Figure B. This is Figure A, this is Figure B. And what I want you to do is given what we're just told, try to figure out what x would be equal to. Pause this video and have a go. All right, now let's do this together.
Now, given that these are scale copies of each other, that means the ratio of corresponding sides would be the same, or any feature, say, distances between points would be the same. So, for example, the distance between this point and this point, which is 18.5, the ratio of that to this side, this side of length 10, would be the same as the ratio of this distance, of the distance of length x to 6.
So, let's just write that out. We could write 18.5 is to 10 as x is to 6. There's other ways that we could have set that up. We could have said that the ratio of x to 18.5, x to 18.5 is equal to the ratio of 6 to 10. Any of these would've set us up, and there's actually other ways we could have done it as well.
So, we could just pick these and pick one of them and solve. So, let's do it with, well, this one's actually pretty straightforward. We just have to multiply both sides by six. So, we get 6 times 18.5 over 10 is equal to x. And let's see if we can do 6 times 18 is 60 plus 40, 808, and then plus three.
Am I doing that, lemme just actually multiply it out, let me not do it all in my head. 18.5 times 6. 5 times 6 is 30, 6 times 8 is 48 plus 3 is 51. 1 times 6 is 6, plus 5 is equal to 11, and then we have one number to behind the decimal, so it's equal to 111, 111 over 10, or another way of thinking about it is 11.1 is equal to x, or x is equal to 11.1 in this scenario.
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