To determine the scale factor for dilating the photo from its original dimensions to the new dimensions, follow these steps:
1. Identify the original dimensions of the photo:
- Original width: [tex]\( 2.5 \)[/tex] inches
- Original height: [tex]\( 3.5 \)[/tex] inches
2. Identify the new dimensions of the photo:
- New width: [tex]\( 5 \)[/tex] inches
- New height: [tex]\( 7 \)[/tex] inches
3. Calculate the scale factor for the width:
- Divide the new width by the original width:
[tex]\[
\text{Scale factor for width} = \frac{\text{New width}}{\text{Original width}} = \frac{5}{2.5} = 2.0
\][/tex]
4. Calculate the scale factor for the height:
- Divide the new height by the original height:
[tex]\[
\text{Scale factor for height} = \frac{\text{New height}}{\text{Original height}} = \frac{7}{3.5} = 2.0
\][/tex]
5. Confirm that both scale factors are equal:
- Since both width and height scale factors are [tex]\( 2.0 \)[/tex], the dilation is proportional.
6. Determine the overall scale factor:
- The scale factor of the dilation is [tex]\( 2.0 \)[/tex].
Thus, the scale factor of dilating the photo from [tex]\( 2.5 \)[/tex] inches by [tex]\( 3.5 \)[/tex] inches to [tex]\( 5 \)[/tex] inches by [tex]\( 7 \)[/tex] inches is [tex]\( 2.0 \)[/tex].
