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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

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