Answer:
To find the scalar factor in the dilation of the given triangle.
The larger triangle is the result of a dilation and translation of the smaller triangle.
we have that,
Scale factor = Dimension of the new shape ÷ Dimension of the original shape
The vertices of the smaller triangle are,
[tex]\begin{gathered} P(1,1) \\ Q(3,1) \\ R(1,3) \end{gathered}[/tex]
PQR be the smaller triangle, by dilation and translation of the smaller triangle we get the larger triangle P'Q'R'.
The transformation occurred as,
[tex]\begin{gathered} P(1,1)\rightarrow P^{\prime}(2,2) \\ Q(3,1)\rightarrow Q^{\prime}(9,2) \\ R(1,3)\rightarrow R^{\prime}(2,9) \end{gathered}[/tex]
we get that,
Length of PQ=2,
Length of P'Q'=7,
Substitute the values in the scalar factor we get,
Scalar factor is,
[tex]=\frac{7}{2}=3.5[/tex]
The required scalar factor is 3.5.
Answer is: 3.5
