#4.5 Dilations

A transformation in which a figure is enlarged or reduced is called a....

• dilation

• reflection

• rotation

• translation

The ratio of the lengths of the corresponding sides of the image and the preimage is called the....

• dilation

• product

• center of dilation

• scale factor

Find the scale factor of the dilation.

• 3

• 
  

  $\frac{1}{3}$
  

• 9

• $\frac{1}{9}$

Is the dilation a reduction or enlargement?

• reduction

• enlargement

Which choice correctly describes the dilation shown here?

• Enlargement by scale factor $\frac{2}{5}$

• Reduction by scale factor 2.5

• Enlargement by scale factor 2.5

• Reduction by scale factor $\frac{2}{5}$

Find the coordinates after a dilation with scale factor 2.

• $\left(4,6\right),\ \left(-6,-2\right),\ \left(4,-2\right)$

• $\left(6,4\right),\ \left(-2,-6\right),\ \left(-2,4\right)$

• $\left(1,\frac{3}{2}\right),\ \left(-\frac{3}{2},-\frac{1}{2}\right),\ \left(1,\ -\frac{1}{2}\right)$

• $\left(\frac{3}{2},1\right),\ \left(-\frac{1}{2},-\frac{3}{2}\right),\ \left(-\frac{1}{2},1\right)$

Identify the scale factor that maps

 $\Delta PQR\ to\ \Delta P'Q'R'$  

• 2

• 3

•  $\frac{1}{3}$  

•  $\frac{1}{2}$  

Find the coordinates of the image of the triangle after a dilation with scale factor k = - 2.

•  $A'\left(-2,-6\right),\ B'\left(4,\ -2\right),\ C'\left(-8,-4\right)$  

•  $A'\left(-6,-2\right),\ B'\left(-2,\ 4\right),\ C'\left(-4,-8\right)$  

•  $A'\left(-\frac{1}{2},-\frac{3}{2}\right),\ B'\left(1,\ -\frac{1}{2}\right),\ C'\left(-2,-1\right)$  

•  $A'\left(-\frac{3}{2},-\frac{1}{2}\right),\ B'\left(-\frac{1}{2},1\right),\ C'\left(-1,-2\right)$  

A sticker can be made in two sizes: 2 x 3 cm and 3 X 4.5 cm. What is the scale factor of the dilation from the smaller to the larger sticker?

• 1.5

• 2

• 2.5

• 3

You are using a magnifying glass that shows the image of an object that is six times the object’s actual size. Determine the length of the image of the spider with length 2.5 mm through the magnifying glass.

• 2.4 mm

• 11.9 mm

• 15 mm

• 37.5 mm