Question

Point A(7,-35) is dilated to A'(1,-5). What is the scale factor and is this a reduction or and enlargement?

Answer 1

Let k be the scale factor.

After dilating A(7,-35) by the scale factor k, its new coordinates are:

$A^{\prime}(7k,-35k)$

On the other hand, the coordinates of A' are given:

$A^{\prime}(1,-5)$

Each coordinate has to be the same in both expressions for A'. then:

$\begin{gathered} 7k=1 \\ \Rightarrow k=\frac{1}{7} \end{gathered}$

Therefore, the scale factor is 1/7.

Since 1/7 < 1, then it is a reduction.