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Which describes the transformation from the original to the image, and tells whether the two figures are similar or congruent?

Which describes the transformation from the original to the image, and tells whether-example-1

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Answer:

(d) reflection, congruent

Explanation:

You want to know the transformation that maps ∆ABC to ∆A'B'C', and whether it keeps the figures congruent.

Rigid transformations

A rigid transformation is one that does not change size or shape. These are ...

  • translation
  • rotation
  • reflection

As a consequence of the size and shape being preserved, the transformed figure is congruent to the original.

Reflection

Just as looking in a mirror reverses left and right, so does reflection across a line in the coordinate plane. The sequence of vertices A, B, C is clockwise in the pre-image. The sequence of transformec vertices, A', B', C' is counterclockwise (reversed) in the image.

This orientation reversal is characteristic of a reflection.

The image is a congruent reflection of the original.

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Additional comment

Dilation changes the size, so the resulting figure is similar to the original, but not congruent. Reflection across a point (rather than a line) is equivalent to rotation 180° about that point.

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