To determine the original dimensions of the photo before it was enlarged, we need to understand the relation between the original and the enlarged photo under the dilation process.
Given:
- The enlarged dimensions of the poster are [tex]\( 24 \times 32 \)[/tex] inches.
- The dilation factor is 4 ([tex]\( D_{Q, 4} \)[/tex]).
Here’s how we find the original dimensions:
1. Identify the enlarged dimensions:
The enlarged photo has dimensions 24 inches in width and 32 inches in height.
2. Understand the dilation factor:
A dilation factor of 4 means each dimension of the original photo is multiplied by 4 to get the enlarged dimensions.
3. Calculate the original dimensions:
- To find the original width, we divide the enlarged width by the dilation factor:
[tex]\[
\text{Original Width} = \frac{24 \text{ inches}}{4} = 6 \text{ inches}
\][/tex]
- To find the original height, we divide the enlarged height by the dilation factor:
[tex]\[
\text{Original Height} = \frac{32 \text{ inches}}{4} = 8 \text{ inches}
\][/tex]
Therefore, the dimensions of the original photo, before it was enlarged, are [tex]\( 6 \times 8 \)[/tex] inches.
So, the correct answer is:
[tex]\[ 6 \times 8 \][/tex]
