Question

The larger triangle in the figure is a result of a dilation and translation of the smaller triangle.

Answer 1

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,

`\begin{gathered} P(1,1) \\ Q(3,1) \\ R(1,3) \end{gathered}`

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,

`\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}`

we get that,

Length of PQ=2,

Length of P'Q'=7,

Substitute the values in the scalar factor we get,

Scalar factor is,

`=(7)/(2)=3.5`

The required scalar factor is 3.5.

Answer is: 3.5