Dilating figures on a circular grid
About this video
Sal finds which image shows quadrilateral EFGH dilated by a scale factor of 2 from center R. He rules out the shrunken image, then checks that each vertex moves twice as far from R, landing on STUV.
You'll be able to
- explain that a scale factor of 2 makes every point twice as far from the center of dilation.
- rule out images that shrink or are distorted.
- check each vertex to confirm the correct dilated image.
Key words
- dilation
- A transformation that makes a figure bigger or smaller using a center and a scale factor.
- center of dilation
- The fixed point that all distances are measured from.
- scale factor
- The number each distance from the center is multiplied by.
- quadrilateral
- A shape with four straight sides.
Transcript
- [Instructor] We're told that quadrilateral EFGH is dilated with a center of dilation at point R. So this is E, F, G, H, this is a center of dilation. Which image represents the dilation of EFGH with a scale factor of two? So pause this video, have a go at that.
Okay. So a scale factor of two, that means we're going to grow. Every point's going to go twice as far from the center of dilation as it was before. So you could immediately rule out anything that would shrink the figure. So we could rule out this W, X, Y, Z. We could also see that W, X, Y, Z doesn't...
Let's see, is it always? And yes, even within itself, it's not the same ratio of distances from the origin. So we can definitely rule that one out. Even if it was the same ratios, we would be dealing with a smaller thing. So that would, even if it had the same ratios, it would be a scale factor less than one.
So now we're left with either this STUV or MNOP. What I could do is just look at each point on our original one, E, F, G, H, and just see where we end up if we go twice as far. So right now, let me get another color here. F is, looks like one, two, three units to the right of our center of dilation.
If we have a scale factor of two, we'll be six units away, twice as far. So three, four, five, six. So I'm already liking STUV, but let's just double check. E was also one, two, three units above the center of dilation. And if we were to go twice that, we would go up to four, five, six.
We would go to S, still looking good. And then we have H was three units to the left, and now we would go six units to the left to V. And then last but not least, G is two units below the center of dilation. So if you go twice as far, because of a scale factor of two, you would go to four units away.
So I am liking STUV. STUV is the image that represents the dilation of EFG with a scale factor of two.
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