A square with vertices at (3,3), (6,3), (6,6), and (3,6) is transformed to a square with vertices at (−3,−3), (−6,−3), (−6,−6), and (−3,−6). Which transformation was applied?

Question

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1 point
Translation 6 units left and 6 units down
Translation 6 units right and 6 units up
Rotation 180 degrees about the origin
Rotation 90 degrees clockwise about the origin

Answer 1

To determine the transformation that takes the original square with vertices at (3,3), (6,3), (6,6), and (3,6) to the new square with vertices at (−3,−3), (−6,−3), (−6,−6), and (−3,−6), we can analyze the coordinates.

1. Original Vertices:

   • (3, 3)
   • (6, 3)
   • (6, 6)
   • (3, 6)

2. Transformed Vertices:

   • (−3, −3)
   • (−6, −3)
   • (−6, −6)
   • (−3, −6)

By comparing the two sets of vertices, we notice that each point in the original square has its coordinates negated:

• (3, 3) becomes (−3, −3)
• (6, 3) becomes (−6, −3)
• (6, 6) becomes (−6, −6)
• (3, 6) becomes (−3, −6)

This indicates that the transformation involved rotating the points 180 degrees about the origin, which essentially flips both the x and y coordinates to their negatives.

Based on this analysis, the correct transformation that was applied is:

Rotation 180 degrees about the origin.