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vova2212 [387]
3 years ago
15

The blue shape is a dilation of the black shape. What is the scale factor of the dilation?

Mathematics
2 answers:
Yakvenalex [24]3 years ago
7 0
4/1 4 is your answer
BabaBlast [244]3 years ago
4 0

Answer:

scale factor = 4

Step-by-step explanation:

The ratio of corresponding sides, blue shape to black shape.

The corresponding widths are 1 and 4 , then

scale factor = \frac{4}{1} = 4

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~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill

\begin{cases} h=3\\ k=-7 \end{cases}\implies y=a(x-3)^2-7\qquad \textit{we also know that} \begin{cases} x=1\\ y=-10 \end{cases} \\\\\\ -10=a(1-3)^2-7\implies -3=a(-2)^2\implies -3=4a\implies -\cfrac{3}{4}=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{3}{4}(x-3)^2-7~\hfill

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