To determine the dimensions of the original photo, we need to understand what the dilation [tex]\( D_{Q, 4} \)[/tex] signifies. The dilation [tex]\( D_{Q, 4} \)[/tex] indicates that the enlargement has been scaled by a factor of 4. This means every dimension of the original photo has been multiplied by 4 to get the dimensions of the enlarged poster.
The dimensions of the enlarged poster are given as 24 inches by 32 inches.
To find the dimensions of the original photo, we will divide each dimension of the enlarged poster by the dilation factor, which is 4.
1. First, let's determine the width of the original photo:
[tex]\[
\text{Original width} = \frac{\text{Enlarged width}}{\text{Dilation factor}} = \frac{24 \text{ inches}}{4} = 6 \text{ inches}
\][/tex]
2. Next, let's determine the height of the original photo:
[tex]\[
\text{Original height} = \frac{\text{Enlarged height}}{\text{Dilation factor}} = \frac{32 \text{ inches}}{4} = 8 \text{ inches}
\][/tex]
Therefore, the dimensions of the original photo are 6 inches by 8 inches.
Among the given options, the correct choice is:
[tex]\[ 6 \times 8 \][/tex]
