The coordinates of trinagle ABC is :
A(2, 1), B(-1, 3), C(-3,-2)
and the coordinates of triangle A'B'C'
A'(4,2) B'(-2,6), C'(-6,-4)
For the dialation, find the constant ratio:
Divide A'/A :
[tex]\begin{gathered} \frac{A^{\prime}}{A}=\frac{(4,2)}{(2,1)} \\ \text{ The ratio of coordinates of A' to A is 2} \\ i\mathrm{}e\text{. A'=2(A)} \end{gathered}[/tex]Now, for the coordinates B,
[tex]\begin{gathered} \frac{B^{\prime}}{B}=\frac{(-2,6)}{(-1,3)} \\ \text{ the ratio of coordinates of B' to B is 2} \\ i\mathrm{}e\text{. B'=2B} \end{gathered}[/tex]Now, for the coordinate C:
[tex]\begin{gathered} \frac{C^{\prime}}{C}=\frac{(-6,-4)}{(-3,-2)} \\ \text{the ratio of coordinates of C' to C is 2} \\ i\mathrm{}e\text{. C' =2C} \end{gathered}[/tex]thus, the scale factor of dialation is 2
Answer : scale Factor = 2