Question

A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the (1.)_____ followed by a translation (2.)_____ .

Answer 1

The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the line (1.) and a translation (2.) .

Step-by-step explanation:

The first transformation, a reflection, involves flipping the original triangle ∆ABC across a specific line, denoted as (1.). This line serves as the axis of reflection, and the resulting triangle is denoted as ∆A′B′C′. The reflection preserves the size and shape of the triangle but changes its orientation.

Following the reflection, the second transformation is a translation. Translation involves moving the reflected triangle horizontally or vertically without changing its orientation. The translation is denoted as (2.), indicating the direction and distance of the shift. The combination of the reflection and translation sequence precisely transforms ∆ABC into ∆A′B′C′.

Understanding these transformations is fundamental in geometry and allows for a precise description of the changes applied to geometric figures. Reflections and translations are part of a broader set of transformations used to analyze and manipulate shapes in mathematical and practical contexts.