Final answer:
The scale factor of the dilation in which point D (4,3) becomes D' (8,6) is 2, as the coordinates of the point are doubled in the dilation.
Step-by-step explanation:
The student is asking about finding the scale factor of a dilation in which point D (4,3) becomes D' (8,6). To find the scale factor, you compare the coordinates of the pre-image with the image. Since both the x-coordinate and y-coordinate of point D are doubled to get D', the scale factor is 2. This means that each dimension in the pre-image is multiplied by 2 to get the corresponding dimension in the image. If we denote the scale factor as 'k', we can set up a proportion for the x-coordinates (4k=8) and for the y-coordinates (3k=6). For both proportions, solving for 'k' would give us a scale factor of 2.
This example shows how to determine a scale factor when given two corresponding points before and after a dilation. In general, if a point (x,y) undergoes dilation to become (x',y'), then the scale factor 'k' is found by dividing one of the image coordinates by the corresponding pre-image coordinate (x'/x or y'/y), assuming that the dilation is centered at the origin and the figures are similar.