Question

Given the triangle ABC with the points A = ( 4, 6 ) B = ( 2, 8 ) C = ( 5, 10 ) and it's dilation, triangle A'B'C', with points A' = ( 2, 3 ) B' = ( 1, 4 ) C' = ( 2.5, 5 ) what is the scale factor?

Answer 1

Step-by-step explanation:

Given A = (4, 6) B = (2, 8) C = (5, 10)

`\begin{gathered} AB=√((2-4)^2+(8-6)^2) \\ \\ =√(8) \\ \\ BC=√((5-2)^2+(10-8)^2) \\ \\ =√(8) \end{gathered}`

SImilarly, for A' = (2, 3) B' = (1, 4) C' = (2.5, 5)

`\begin{gathered} A^(\prime)B^(\prime)=√((1-2)^2+(4-3)^2) \\ \\ =√(2) \\ \\ B^(\prime)C^(\prime)=√((2.5-1)^2+(5-4)^2) \\ \\ =√(3.25) \end{gathered}`

Since it is a dilation, AB/A'B' should be the same as BC/B'C', but that is not the case here.