∆PQR has vertices at P(2, 4), Q(3, 8) and R(5, 4). A dilation and series of translations map ∆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?
Answers
Given : ∆PQR has vertices at P(2, 4), Q(3, 8) and R(5, 4). A dilation and series of translations map ∆PQR to ∆ABC, whose vertices are A(2, 4), B(5.5, 18), and C(12.5, 4).
To Find : Scale factor of the dilation in the similarity transformation
Solution:
P(2, 4), Q(3, 8) and R(5, 4)
PQ = √(3-2)² + (8 - 4)² = √17
PR = √(5-2)² + (4 - 4)² = 3
QR = √(5-3)² + (4 - 8)² = 2√5
A(2, 4), B(5.5, 18), and C(12.5, 4)
AB = √(5.5-2)² + (18 - 4)² = 3.5√17
AC = √(12.5-2)² + (4 - 4)² = 10.5
BC = √(12.5-5.5)² + (4 - 18)² = 7√5
AB/PQ = AC/PR = BC/QR = 3.5
scale factor of the dilation in the similarity transformation = 3.5
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