Question

question 9
triangle abc is formed by a reflection over x = -3 and dilation by a scale factor of 3 from the origin. which equation shows the correct relationship between △abc and △abc?
\\(\frac{bc}{bc}=\frac{1}{3}\\)
\\(\frac{ab}{ab}=\frac{1}{3}\\)
\\(ac = 3ab\\)
\\(ab=3bc\\)

Explanation:

Step1: Recall dilation property

When a figure is dilated by a scale factor \(k\) from the origin, the lengths of the corresponding sides of the original figure and the dilated figure are related by the ratio \(\frac{\text{length in dilated figure}}{\text{length in original figure}}=k\). Here \(k = 3\). So, if we consider two corresponding sides, say \(AB\) of \(\triangle ABC\) and \(A'B'\) of \(\triangle A'B'C'\), we have \(\frac{A'B'}{AB}=3\), which can be rewritten as \(\frac{AB}{A'B'}=\frac{1}{3}\).

Step2: Analyze other - side - length ratios

For any pair of corresponding sides of \(\triangle ABC\) and \(\triangle A'B'C'\), the ratio of the side - length of \(\triangle ABC\) to the side - length of \(\triangle A'B'C'\) is \(\frac{1}{3}\) because of the dilation by a scale factor of 3.

Answer:

\(\frac{AB}{A'B'}=\frac{1}{3}\)