Question

a horizontal line m is shown with two similar triangles, abc and def. how can triangle abc be transformed to result in triangle def? a a dilation, then a reflection across a vertical line b a dilation, then a translation to the right c a 90 - degree rotation about point c d a reflection across a vertical line

Explanation:

Step1: Analyze dilation

Since the triangles are similar but of different sizes, a dilation (scaling) must be involved. Dilation changes the size of a figure while keeping its shape.

Step2: Analyze translation

After dilation, we observe the position of the triangles. There is no reflection (as the orientation of the triangles relative to the horizontal line \(m\) is the same in a sense of left - right orientation after considering size change, and no rotation about point \(C\) would map \(ABC\) to \(DEF\) in terms of position and size). A translation to the right is needed to move the dilated triangle from the position of \(ABC\) (after dilation) to the position of \(DEF\).

Answer:

B. a dilation, then a translation to the right