Exercise 12 Page 597

We are asked to determine if the yearbook photo is a dilation of the original photo. To do this, we will compare a ratio of widths and a ratio of lengths. If they turn out to be equal, then we have a dilation. Yearbook's Width/Original Width? =Yearbook's Length/Original Length Let's evaluate these ratios using the given dimensions. We will start with the ratio of widths.

Yearbook's Width/Original Width

SubstituteII

Yearbook's Width= 6 23, Original Width= 4

6 23/4

▼

Simplify

MixedToFrac

a bc=a* c+b/c

203/4

DivFracSL

.a/b /c.= a/b* c

20/3*4

Multiply

Multiply

20/12

ReduceFrac

a/b=.a /4./.b /4.

5/3

The ratio of widths is 53. Now we will evaluate the ratio of lengths.

Yearbook's Length/Original Length

SubstituteII

Yearbook's Length= 10, Original Length= 6

10/6

ReduceFrac

a/b=.a /2./.b /2.

5/3

The ratio of lengths is also 53. Yearbook's Width/Original Width? =Yearbook's Length/Original Length ⇓ 5/3=5/3 Since the ratios are equal, the yearbook photo is a dilation of the original photo, and the scale factor is 53.