Final answer:
The scale factor for dilating segment AB to create segment A'B' with given coordinates is 1:4, which means the figure is enlarged by a factor of 4. To use this in a proportion, set up the ratio 1:2 = 4:x and solve for x to find the increased dimension.
Step-by-step explanation:
The student has asked about finding the scale factor used in dilating segment AB to create segment A'B'. With coordinates A' (0, 4) and B' (4, 6), we must compare these to the original segment coordinates which are not provided in the question. However, we can approach this by identifying the ratio of the coordinates of A' and B' to that of AB. Since the point A' is at (0, 4), if we consider the origin as the center of dilation, the dilation factor is the distance from the origin to A' divided by distance from the origin to A, which would be considered as 1 in this context since it will be a unit fraction. Therefore, if A' is 4 units away from the origin after dilation, then the scale factor is 1:4 or simply, a scale factor of 4.
To apply this information to a proportion such as 1:2 = 4:x, we solve for x by cross-multiplying and find that x is 8. This means that if the scale dimension is 4, the actual dimension is 8 times larger, indicating that the actual dimension will increase by a factor of eight. When dealing with different scale factors and measurements, it's crucial to set up the appropriate proportion and solve for the missing variable to find the actual dimensions.