Question

You are making a poster to support your friend for homecoming. Your original photo is 3 inches by 5 inches. You want the photo on the poster to be 2 1/2 feet by 4 1/6 feet. What is the scale factor of this dilation?

Answer 1

To find the scale factor for enlarging a photo from 3 inches by 5 inches to 2 1/2 feet by 4 1/6 feet, first convert feet to inches and then compare the dimensions of both photos. The scale factor is 10, as both width and height are enlarged by a factor of 10.

Step-by-step explanation:

You are making a poster and need to determine the scale factor for resizing a photo from 3 inches by 5 inches to 2 1/2 feet by 4 1/6 feet. To find the scale factor, you compare the dimensions of the enlarged photo to the original photo.

First, convert the measurements of the larger photo from feet to inches, since the original photo is in inches (1 foot = 12 inches):
2 1/2 feet = 2.5 * 12 inches = 30 inches
4 1/6 feet = (4 + 1/6) * 12 inches = (4 * 12) + (1/6 * 12) inches = 48 + 2 inches = 50 inches.

Next, calculate the scale factor for each dimension separately and check that they are consistent:
Scale factor for width = 30 inches / 3 inches = 10
Scale factor for height = 50 inches / 5 inches = 10

Since both width and height have the same scale factor of 10, the overall scale factor for the dilation is 10.

Answer 2

9

Step-by-step explanation:

We have been given that dimensions of original photo are 4 inches by 6 inches. We want the photo on the poster to be of dimensions 3 feet by 4 1/2 feet.

First of all we will convert dimensions of poster from feet to inches.

3ft = 3x12 in = 36ft

4 1/2 ft = 4.5x 12in = 54in

Now let us compare sides of our original photo with corresponding sides of poster.

frac{36}{4} = 9

Now let us compare the second pair of corresponding sides.

\frac{54}{6} =9

We have seen that sides of poster are 9 times the sides of our original photo, therefore, the scale factor of this dilation is 9.