Question

sylvia enlarged a photo to make a 24 x 32 inch poster using the dilation ( d_{q,4} ). what are the dimensions, in inches, of the original photo?
( \bigcirc ) ( 3 \times 8 )
( \bigcirc ) ( 6 \times 8 )
( \bigcirc ) ( 12 \times 16 )
( \bigcirc ) ( 18 \times 24 )

Explanation:

Step1: Recall Dilation Scale Factor

Dilation \( D_{Q,4} \) means the scale factor \( k = 4 \) (enlargement, so original dimensions are poster dimensions divided by 4).

Step2: Calculate Original Length

Poster length is 32 in. Original length: \( \frac{32}{4}=8 \) in.

Step3: Calculate Original Width

Poster width is 24 in. Original width: \( \frac{24}{4}=6 \) in.

Answer:

6 × 8 (Option B if options are labeled, but here the correct dimensions are 6×8)