Answered

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?

Verified Answer :

MissPhiladelphia

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

Answer:

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

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