Final answer:
The scale factor r of the dilation, given |OA| = 5 and OA' = 7.5, is calculated by dividing the length of OA' by the length of OA, resulting in r = 1.5.
Step-by-step explanation:
The student has asked about the determination of a scale factor in the context of a geometric dilation. In this scenario, the original length of segment OA is 5 units, and after dilation, the length of OA' is 7.5 units. To find the scale factor, noted as r, we need to divide the length of the dilated segment by the original length of the segment.
The calculation is simple:
r = |OA'| / |OA| = 7.5 / 5 = 1.5
Therefore, the scale factor of the dilation is 1.5.