7.11. Dilation http://www.ck12.org
If the scale factor is 3 andQis 6 units away fromP, thenQ′is going to be 6× 3 =18 units away fromP. Because
we are only dilating apoint, the dilation will be collinear with the original and center.
Example B
Using the picture above, change the scale factor to^13. FindQ′′.
Now the scale factor is^13 , soQ′′is going to be^13 the distance away fromPasQis. In other words,Q′′is going to be
6 ×^13 =2 units away fromP.Q′′will also be collinear withQand center.
Example C
KLMNis a rectangle with length 12 and width 8. If the center of dilation isKwith a scale factor of 2, drawK′L′M′N′.
IfKis the center of dilation, thenKandK′will be the same point. From there,L′will be 8 units aboveLandN′will
be 12 units to the right ofN.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter7DilationB
Vocabulary
Adilationan enlargement or reduction of a figure that preserves shape but not size. All dilations are similar to the
original figure.Similarfigures are the same shape but not necessarily the same size. Thecenter of a dilationis the
point of reference for the dilation and thescale factorfor a dilation tells us how much the figure stretches or shrinks.
Guided Practice
- Find the perimeters ofKLMNandK′L′M′N′. Compare this ratio to the scale factor.
- 4 ABCis a dilation of 4 DEF. IfPis the center of dilation, what is the scale factor?
- Find the scale factor, given the corresponding sides. In the diagram, theblackfigure is the original andPis the
center of dilation.
Answers:
- The perimeter ofKLMN= 12 + 8 + 12 + 8 =40. The perimeter ofK′L′M′N′= 24 + 16 + 24 + 16 =80. The ratio
is 80:40, which reduces to 2:1, which is the same as the scale factor. - Because 4 ABCis a dilation of 4 DEF, then 4 ABC∼4DEF. The scale factor is the ratio of the sides. Since
4 ABCis smaller than the original, 4 DEF, the scale factor is going to be less than one,^1220 =^35.
If 4 DEFwas the dilated image, the scale factor would have been^53.
- Since the dilation is smaller than the original, the scale factor is going to be less than one. 208 =^25