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How would you describe this series of transformations?

(1 point)

Reflection across the y-axis and then a translation of (-3,-5) shows that triangle ABC is congruent to triangle AB C

Since triangles ABC and A"B" C" do not have the same orientation, they are not congruent.

Rotation of 30 degrees clockwise and then reflection across the z-axis shows that triangle ABC is congruent to triangle A"B" C

Translation of (2,0) and then reflection across the r-axis shows that triangle ABC is congruent to triangle

ABC"

1 answer

The transformations described involve various geometric operations applied to triangle ABC, leading to comparisons of congruence between triangle ABC and its transformed images.

  1. Reflection Across the Y-Axis and Translation (-3, -5): This operation indicates that the triangle is flipped across the y-axis and then moved. Although the shapes of triangles ABC and A"B"C" are identical, their different orientations (one being a mirror image) indicate that they are not congruent despite having the same size and shape.

  2. Rotation of 30 Degrees Clockwise and Reflection Across the Z-Axis: Here, the triangle is first rotated, and then a reflection is applied. As a result, we conclude that triangle ABC remains congruent to triangle A"B"C. This is because rotations and reflections preserve the shape and size of the triangle.

  3. Translation of (2,0) and Reflection Across the R-Axis: This transformation shifts the triangle to a new position and then reflects it across an axis. The description implies that the resulting triangle, ABC", retains congruence with triangle ABC, as translations and reflections also preserve size and shape.

In summary, congruence is maintained through certain transformations, including rotations, translations, and reflections, but orientation affects whether two objects are congruent or merely identical. Triangles can be congruent but not congruent in orientation, as demonstrated in the various transformation scenarios presented.