Identifying scale factors

So right over here, figure B is a scaled copy of figure A. What we want to do is figure out what is the scale factor to go from figure A to figure B. Pause the video and see if you can figure that out.

Well, all we have to do is look at corresponding sides and think about how much they have been scaled by. So, for example, this side right over here would correspond to this side right over here on figure B. Over here, it had length two, and over here, it has length one, two, three, four, five, six. So, it looks like that side has been scaled up by a factor of three.

If figure B truly is a scaled copy, then every side should be scaled up by a factor of three. We could verify that; we don't have to do it with every side. We're being told that these are scaled copies, but we can see that this is the case. For example, this side right over here corresponds to this base right over here. This has length three.

So, if we're scaling up by a factor of three, we should multiply that by three, and this should be of length nine. Let's see if that's the case: one, two, three, four, five, six, seven, eight, and nine. You can see we can feel pretty good that figure B is a scaled copy of figure A, and that scaling factor is three.

Let’s do another example. Here we are told Ismail made a scaled copy of the following quadrilateral. He used a scale factor less than one. All right, and then they say, what could be the length of the side that corresponds to AD?

So, AD is right over here. AD has length 16 units in our original quadrilateral. What could be the length of the side that corresponds with AD on the scaled copy of the quadrilateral? Since it's a scale factor less than one, we're going to get something that is less than 16 for that side. The rest of it will all be scaled by the same factors.

So, the resulting quadrilateral might look something like this; this is just my hand-drawn version. The key realization is if our scale factor is less than 1, this thing right over here is going to be less than 16 units.

So, let's look at the choices, and it says choose three answers. Pause the video. Which of these would match if we're scaling by a factor of less than one? Well, we just have to see which of these are less than 16 units. This is less than 16; this is less than 16; this is less than 16. Those are the only three that are less than 16.

32 units would be a scale factor of 2. 64 units would be a scale factor of 4, clearly a scale factor that is not less than 1.