Question

determine the similarity transformations that verify \\( \triangle abc - \triangle a ^ { \prime \prime } b ^ { \prime \prime } c ^ { \prime } \\) the first transformation mapping \\( \triangle abc \\) to \\( \triangle a ^ { \prime } b ^ { \prime } c ^ { \prime } \\) is a the second transformation mapping \\( \triangle a ^ { \prime } b ^ { \prime } c ^ { \prime } \\) to \\( \triangle a ^ { \prime \prime } b ^ { \prime \prime } c ^ { \prime } \\) is a x rotation of 90 degrees about \\( b ^ { \prime } \\) reflection across \\( a ^ { \prime } b ^ { \prime } \\) dilation with center \\( c ^ { \prime } \\) translation left

Explanation:

Step1: Analyze the first transformation

By observing the positions of \(\triangle ABC\) and \(\triangle A'B'C'\), we can see that \(\triangle ABC\) is moved to the left to get \(\triangle A'B'C'\). This is a translation transformation.

Step2: Analyze the second transformation

From \(\triangle A'B'C'\) to \(\triangle A''B''C'\), the size of the triangle changes while the point \(C'\) remains fixed. This is a dilation transformation with center \(C'\) (because the shape is similar and one - point remains in place while the other points move proportionally).

Answer:

The first transformation: translation left; The second transformation: dilation with center \(C'\)