Question

PQR has vertices at P(2, 4), Q(3, 8) and R(5, 4). A similarity transformation maps PQR to ABC, whose vertices are A(2, 4), B(5.5, 18), and C(12.5, 4). What is the scale factor of the dilation in the similarity transformation?

Answer 1

3.5 is the correct answer just had question and it was correct

Explanation:

Answer 2

Use Pythagorean Theorem to calculate length of sides

PQ = √(1^2 + 4^2) = √(17)
QR = √(2^2 + 4^2) = √(20)
RP = √(3^2 + 0^2) = √(9)

AB = √(3.5^2 + 14^2) = √(208.25)
BC = √(7^2 + 14^2) = √(245)
CA = √(10.5^2 + 0^2) = √(110.25)

A similarity transformation will maintain the relationship of sides: the smallest side of one triangle should correspond to the shortest side of the other triangle (and so on).

Ratio of lengths (transformed/original)

shortest with shortest
CA/RP = √(110.25)/√(9) = 10.5/3 = 3.5
middle
AB/PQ = √(208.25)/√(17) = √(208.25/17) = √(12.25) = 3.5
longest
BC/QR = √(245)/√(20) = √(12.25) = 3.5