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Grade 8 · Spatial Sense · Tessellations, Views, and Transformations

Transform and Reconstruct Shapes

Transformations describe how a figure moves or changes size. Multiple two-dimensional views can also provide enough information to build a three-dimensional model.

The big idea

Properties reveal what changed and what stayed invariant

Translations, reflections, and rotations preserve lengths and angles. Dilations preserve angles but scale lengths. Tessellations use transformations without gaps or overlaps.

Work it through

Dilate (−3, 4) by scale factor 2 about the origin

  1. 1. Multiply each coordinate by the scale factor.
  2. 2. x becomes −3 × 2 = −6.
  3. 3. y becomes 4 × 2 = 8.
  4. 4. The image point is (−6, 8); direction is preserved and distance from the origin doubles.