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Sylvia enlarged a photo to make a 24 × 32 inch poster using the dilation D(Q, 4). What are the dimensions, in inches, of the original photo?

A. 3 × 8
B. 6 × 8
C. 12 × 16
D. 18 × 24

Sagot :

GinnyAnswer
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]
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