Final answer:
To find the scale factor in dilations, identify the ratio of the image's dimensions to the pre-image's dimensions. Multiply the original dimensions by this factor to get the dilated dimensions, or alternatively, set up a proportion to solve for unknown dimensions using the scale factor.
Step-by-step explanation:
When you want to find the scale factor of a dilation, you look for the ratio that compares the dimensions of an image to its pre-image. For example, if you're given that the dimensions of a larger square are twice the dimensions of the first square, the scale factor is 2. This is calculated by multiplying the side length of the first square by 2. So, if the original side length is 4 inches, the dilated square's side would be 4 inches x 2 = 8 inches.
To apply this to other problems, you can set up a proportion using the scale factor and the given dimensions. For instance, if the scale dimension is 4 and the scale factor is 1:2, the proportion would be 1:2 = 4:x, where x represents the missing actual dimension. You can solve for 'x' to find the actual size of the object.
Remember, the scale dimension refers to the model's measurement, while the actual dimension refers to the real-world measurement. In problems involving different units, like converting between inches and feet, it's important to maintain consistent units when writing your proportions.