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D, E and F are the midpoints of BC, CA, and AB respectively. A dilation maps triangle ABC to triangle AFE. What is the scale factor of this dilation?

 

 
 Nov 21, 2020
 #1
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E  is the midpoint of  AC,  so  AE  is half the length of  AC,  or   AE  =  1/2 * AC

 

One way to find the scale factor from  △ABC  to  △AFE  is to find  AE / AC

 

AE / AC   =   (1/2 * AC) / AC   =   1/2

 

So the scale factor is 1/2

 

(Remember the scale factor is the number which each side of the starting triangle must be multiplied by in order to make it the same size as the "goal" triangle. In this case, each side of △ABC must be multiplied by 1/2 to make it the same size as △AFE.)

 
 Nov 21, 2020
 #2
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In this case, the center of dilation is, at the same time, the centroid of both triangles.

 

The triangle DEF is turned upside-down, and that makes the scale factor negative. 

 

The scale factor is -1/2

 
 Nov 21, 2020

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