Question

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

Answer 1

(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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