Question

After a dilation with center (0,0), the image of DB is D'B'. IDB = 4.5 and D'B' = 18, the scale factor of this dilation is (1) (3) (2) 5 (4) 4

Answer 1

We can write the length of DB like this:

$4.5=\frac{9}{2}$

Now, to find the scale factor of the dilation, we have to solve for k the following equation:

$\frac{9}{2}k=18$

then, we have the following:

$\begin{gathered} \frac{9}{2}k=18 \\ \Rightarrow9k=18\cdot2=36 \\ \Rightarrow k=\frac{36}{9}=4 \\ k=4 \end{gathered}$

therefore, the scale factor is k=4