Marcia developed a roll of film and received 4-inch by 6-inch prints. She wants to have one picture enlarged to an 8-inch by 12-inch print. What kind of transformation is this? What is the scale factor?

8/4=2

12/6=2

Area of first rectacangle:

A1=4*6=24

Area of second rectacangle:

A2=8*12=96

96/24=4

Scale for dimensions 2
Scale for areas 4

The transformation is a dilation, specifically an enlargement.

To find the scale factor, we can compare the corresponding dimensions of the original and enlarged prints.

The original print size is 4 inches by 6 inches.
The enlarged print size is 8 inches by 12 inches.

To find the scale factor, we divide the corresponding dimensions:

For the width:
Scale factor = 8 inches (new width) ÷ 4 inches (original width) = 2

For the height:
Scale factor = 12 inches (new height) ÷ 6 inches (original height) = 2

Since both the width and height have a scale factor of 2, the scale factor for the enlargement is 2.

To determine the kind of transformation and scale factor involved in enlarging the picture, we need to consider the change in dimensions.

The original print size is 4 inches by 6 inches, and the desired print size is 8 inches by 12 inches. We can compare the change in dimensions to determine the transformation.

First, calculate the change in width:
Desired Width - Original Width = 8 inches - 4 inches = 4 inches

Next, calculate the change in height:
Desired Height - Original Height = 12 inches - 6 inches = 6 inches

Since both the change in width and height are positive values, we can conclude that this is an enlargement.

To find the scale factor, divide the desired dimensions by the original dimensions in each respective direction.

Scale factor of width = Desired Width / Original Width = 8 inches / 4 inches = 2
Scale factor of height = Desired Height / Original Height = 12 inches / 6 inches = 2

Since both scale factors are the same (2), we can conclude that the enlargement is a uniform or proportional transformation.