Question

Describe the composite transformation that has occurred.

Answer 1

Answer:

• rotate CCW 90°, reflect across the x-axis
• (x, y) ⇒ (-y, -x) . . . . . both transformations together

Step-by-step explanation:

The vertex order ABC is clockwise in the original figure and also in the first image: A'B'C'. The altitude from AC to B is up in the original and left in the first image, indicating a rotation 90° CCW.

  The first transformation is a rotation 90° CCW.

The vertex order of A''B''C'' is CCW, indicating a reflection. The direction of the altitude from A''C'' to B'' is still to the left, so the reflection must be over a horizontal line. We find the x-axis bisects the segments A'A'', B'B'', and C'C'', confirming that it is the line of reflection.

  The second transformation is reflection across the x-axis.

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Algebraically, the transformations are ...

  1st: (x, y) ⇒ (-y, x)

  2nd: (x, y) ⇒ (x, -y)

Both together: (x, y) ⇒ (-y, -x).