Question

triangle a\b\c\ is formed by a reflection over x = 1 and dilation by a scale factor of 2 from the origin. which equation shows the correct relationship between δabc and δa\b\c\?

Explanation:

Step1: Recall transformation properties

A reflection is a rigid - motion which preserves shape and size (congruence), and a dilation changes the size of a figure. A dilation by a scale factor \(k\) from the origin multiplies the coordinates of each point of the pre - image by \(k\). Here \(k = 2\). When we have a sequence of a reflection (a congruence transformation) and a dilation (a similarity transformation), the pre - image \(\triangle ABC\) and the image \(\triangle A''B''C''\) are similar.
The general rule for similar triangles is that if \(\triangle ABC\) and \(\triangle A'B'C'\) are similar, then \(\triangle ABC\sim\triangle A'B'C'\). In our case, \(\triangle ABC\sim\triangle A''B''C''\) because of the reflection (which is a congruence transformation) followed by a dilation (which creates a similar figure).

Answer:

\(\triangle ABC\sim\triangle A''B''C''\)