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Grade 6 · Spatial Sense · Geometry and Transformations

Transform Shapes on the Plane

Coordinates precisely describe location. Transformation rules predict how every point of a shape moves.

The big idea

Apply the same transformation to every vertex

Reflecting across the y-axis changes (x, y) to (−x, y). A 90° counter-clockwise rotation about the origin changes it to (−y, x).

Work it through

Transform the point (4, −2)

  1. 1. Reflect across the y-axis: (4, −2) becomes (−4, −2).
  2. 2. Rotate the reflected point 90° counter-clockwise.
  3. 3. Use (x, y) → (−y, x): (−4, −2) becomes (2, −4).
  4. 4. Check that distance from the origin is preserved.