Answer: The correct option is (d) 3.5.
Step-by-step explanation: Given that triangle PQR has vertices at P(2, 4), Q(3, 8) and R(5, 4). A similarity transformation maps triangle PQR to triangle ABC, whose vertices are A(2, 4), B(5.5, 18), and C(12.5, 4).
We are to find the scale factor of the similarity transformation.
Scale factor of a dilation is defined as
In ΔABC and ΔPQR, the corresponding side of BC is QR.
Now, the lengths of the sides QR and BC are calculated using the distance formula as follows:
Therefore, the sale factor of dilation from ΔPQR to ΔABC is
Thus, the required scale factor is 3.5.
Option (d) is correct.