Question

This diagram shows a pre-image △ABC , and its image, △A′′B′′C′′ , after a series of transformations.

Select from the drop-down menus to correctly complete the statements.

△ABC is

Answer 1

Hello there,

This diagram shows a pre-image △ABC , and its image, △A′′B′′C′′ , after a series of transformations.

Select from the drop-down menus to correctly complete the statements.

△ABC is reflected across the line y = x

to become △A′B′C′ . Then △A′B′C′ is reflected across the x-axis

△A′′B′′C′′ . Because the transformations are both rigid

, the pre-image and image are congruent.

Answer 2

Answer:

△ABC is first reflected across the line y=x, then reflected across the x-axis.  Since the transformations are rigid, △ABC ≅ △A''B''C''.

Step-by-step explanation:

Comparing △ABC and △A'B'C', we see that the x- and y-coordinates have been switched.  This describes a reflection across the line y=x.

Comparing △A'B'C' and △A''B''C'', we see that the y-coordinates have been negated.  This describes a reflection across the x-axis.

Reflections are called rigid transformations.  This is because they preserve congruence and shape.  Since congruence is preserved, △ABC ≅ △A''B''C''.