How do you determine the scale factor used to create the image?

You determine the scale factor by comparing corresponding lengths between the original object and its image.

Here's a breakdown of the process:

1. Identify Corresponding Sides: First, you need to find pairs of sides that correspond to each other in the original shape and the image. Corresponding sides are sides that occupy the same relative position in both shapes.

2. Measure the Corresponding Sides: Once you've identified a pair of corresponding sides, measure their lengths. Make sure you use the same units for both measurements (e.g., inches, centimeters).

3. Calculate the Scale Factor: Divide the length of the side in the image (the enlarged or reduced shape) by the length of the corresponding side in the original shape.

   • Scale Factor = (Length of side in the image) / (Length of side in the original shape)

4. Interpret the Scale Factor:

   • If the scale factor is greater than 1, the image is an enlargement of the original.
   • If the scale factor is less than 1 (but greater than 0), the image is a reduction of the original.
   • If the scale factor is equal to 1, the image is the same size as the original.

Example:

Let's say you have an original square with sides of 2 inches. Its image is a square with sides of 6 inches.

1. Corresponding Sides: A side of the original square corresponds to a side of the image square.

2. Measurements: Original square side = 2 inches; Image square side = 6 inches.

3. Scale Factor: Scale Factor = 6 inches / 2 inches = 3

4. Interpretation: The scale factor is 3, which means the image is an enlargement of the original by a factor of 3.

In essence, the scale factor tells you how much larger or smaller the image is compared to the original. By dividing the length of a side in the new image by the length of its corresponding side in the original, you can find the factor that was used to scale the original figure.