Dilating figures with no grid
About this video
Sal looks at figure G and two dilated images, F and H, with center P. Because F is smaller and closer to P its scale factor is less than 1 (about one half), while H is bigger and further away, so its scale factor is greater than 1; a scale factor of exactly 1 would leave G unchanged.
You'll be able to
- tell whether a dilation's scale factor is less than, equal to, or greater than 1 by looking at the image.
- estimate a scale factor by comparing distances from the center of dilation.
Key words
- dilation
- A transformation that makes a figure bigger or smaller from a center point.
- center of dilation
- The fixed point distances are measured from.
- scale factor
- The number distances from the center are multiplied by; less than 1 shrinks, greater than 1 enlarges.
Transcript
- [Instructor] We're told that Crystal drew figure G and its dilated images with the center of dilation at point P. So G here is I guess the original and then the images of G after dilation are both F and H. So then they're going to make us answer some questions about it.
But before we even do that, let's just think about what happened. If the center of dilation of, if the center of dilation is P, then when we dilated to F, we definitely had a scale factor less than one. If you had a scale factor exactly at one, G would just map right onto itself.
But with a scale factor less than one, each point would get closer to P and the shape would get smaller. And if we, if we were to say this point right over here, this bottom left corner, it goes from there to there. It looks like it goes, it almost covers half the distance.
So this is probably a scale factor of one half. The distance from this point to P went by a half. And it looks like going from G to H, it might be double. If we look at this bottom left corner again, the distance from P looks like it almost doubled. And it looks like the entire thing increased in scale as well.
Now let's answer the questions. So they are telling us, it's this gray color here. Figure F is the dilated image of G with the scale factor. I said it looks like it's about a scale factor about one half. Less than one, yes, less than one. Figure H is the dilated image of G with the scale factor of greater than one.
And if we had equal to one, that would just be G itself. And we're done.
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