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  • - [Instructor] We are told triangle

  • A-prime, B-prime, C-prime is the image

  • of triangle ABC under a dilation

  • whose center is P and scale factor is 3/4.

  • Which figure correctly shows triangle

  • A-prime, B-prime, C-prime using the solid line.

  • So pause this video and see

  • if you can figure this out on your own.

  • All right, now before I even look at the choices,

  • I like to just think about,

  • what would that dilation actually look like?

  • So our center of dilation is P.

  • And it's a scale factor of 3/4.

  • So one way to think about it is,

  • however far any point was from P before,

  • is now going to be 3/4 as far, but along the same line.

  • So I'm just going to estimate it.

  • So if C was there, 3/2 would be this far.

  • So 3/4 would be right about there.

  • So C-prime should be about there.

  • If we have this line connecting B and P like this,

  • let's see, half of that is there.

  • 3/4 is going to be there.

  • So B-prime should be there.

  • And then on this line, halfway is roughly there.

  • I'm just eyeballing it.

  • So 3/4 is there.

  • So A-prime, A-prime, should be there.

  • And so A-prime, B-prime, C-prime

  • should look something like this.

  • Which we can see is exactly what we see for choice C.

  • So choice C, it looks correct.

  • So I'm gonna just circle that,

  • or select it just like that.

  • But let's just make sure we understand why

  • these other two choices were not correct.

  • So choice A, it looks like it is a dilation

  • with a 3/4 scale factor.

  • Each of the dimensions, each of the sides

  • of these triangles, of this triangle,

  • looks like it's about 3/4 of what it originally was.

  • But it doesn't look like the center of dilation is P.

  • Here the center of dilation looks

  • like it is probably the midpoint of segment AC.

  • Because now it looks like everything is 3/4

  • of the distance it was to that point.

  • So they have this other center of dilation in choice A.

  • The center of dilation is not P,

  • and that's why we can rule that one out.

  • And then for choice B right over here,

  • it looks like they just got the scale factor wrong.

  • Actually they got the center of dilation

  • and the scale factor wrong.

  • It still looks like they are using this

  • as a center of dilation.

  • But this scale factor looks like it's much closer

  • to 1/4 or 1/3, not 3/4.

  • So that's why we can rule that one out as well.

  • We like our choice, C.

- [Instructor] We are told triangle


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B1 中級

三角形的擴張:找錯誤 (Dilating triangles: find the error)

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    林宜悉 發佈於 2021 年 01 月 14 日