Question

triangle abc was dilated and translated to form similar triangle abc. what is the scale factor of the dilation?
\\( \frac { 1 } { 5 } \\)
\\( \frac { 2 } { 5 } \\)
\\( \frac { 5 } { 2 } \\)
\\( \frac { 5 } { 1 } \\)

Explanation:

Step1: Find the length of corresponding sides

In triangle \(ABC\), \(BC = 2\) units (from \(y = 2\) to \(y = 0\) at \(x = 2\)). In triangle \(A'B'C'\), \(B'C'=5\) units (from \(y=- 2\) to \(y=-7\) at \(x=-1\)).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the ratio of the length of a side of the image to the length of the corresponding side of the pre - image. So \(k=\frac{B'C'}{BC}\). Substituting the values, we get \(k = \frac{5}{2}\).

Answer:

\(\frac{5}{2}\)