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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
1. reflected across the y-axis.
2. rotated 90 degrees counterclockwise about the origin.
3. translated 4 units right

to become △A′B′C′. Then ​△A′B′C′​ is

1. reflected across the x-axis.
2. reflected across the line y = x
3. rotated 90 degrees counterclockwise about the origin

to become ​△A′′B′′C′′​ . Because the transformations are
1. both rigid
2.not both rigid,

The pre-image and image are

1. congruent
2. not congruent

This diagram shows a preimage ABC and its image ABC after a series of transformations Select from the dropdown menus to correctly complete the statements ABC is class=

Respuesta :

Using translation concepts, we have that:

  • △ABC is 3. translated 4 units right to become △A′B′C′.
  • Then, △A′B′C′​ is 3. rotated 90 degrees counterclockwise about the origin to become △A′′B′′C′′​ .
  • Because the transformations are both rigid, the pre-image and the image are congruent.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

On the translation of △ABC to △A′B′C′, the rule applied to the vertices is:

(x,y) -> (x + 4, y).

Hence it was translated 4 units right.

On the translation of △A′B′C′​ to △A′′B′′C′', the rule is given by:

(x,y) -> (-y,x).

Hence it was rotated 90 degrees counterclockwise about the origin.

The triangle keeps the same size after the translations, hence:

Because the transformations are both rigid, the pre-image and the image are congruent.

More can be learned about translations at https://brainly.com/question/4521517

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