Final answer:
The scale factor for the blue triangle dilated from the red triangle is 'None of the above' because the given scale factor is 1/4. To find a missing actual dimension, a proportion must be set up using the scale factor. The ratio of areas of similar figures is the square of the scale factor.
Step-by-step explanation:
The question asks about the scale factor for a dilation from a red triangle to a blue triangle. The scale factor represents the ratio of the dimensions of the blue triangle to the dimensions of the red triangle in such transformations. In other words, it is the number by which all dimensions of the original figure are multiplied to get the dimensions of the new figure. The correct answer is 'None of the above' since the provided scale factor was 1/4, which is not one of the options listed.
To solve a problem involving a scale factor and finding a missing actual dimension, set up a proportion based on the given scale factor. For instance:
Proportion example: If the scale factor is 2":3' and the scale measurement is 6", then the proportion would be 2 inches / 3 feet = 6 inches / x feet. Solve for x to find the actual dimension.
Applying the Scale Factor
In terms of the area, when comparing areas of similar figures, the ratio of the areas is the square of the scale factor. For example, if the scale factor is 2, then the area of the larger figure would be 2^2 = 4 times the area of the smaller figure.