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?

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

susie1968 susie1968 · Answer 2 · 2018-12-23T18:17:23+01:00

susie1968 susie1968

23-12-2018

Answer:

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

Step-by-step explanation:

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