Math Lesson

Transformations on the Coordinate Plane: Translations, Reflections, and Rotations

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10th GradeBTC Style / Thinking ClassroomsHSG-CO50 min
Learning Objective

Students will apply transformation rules (translations, reflections, rotations) to figures on the coordinate plane, describe transformations using coordinate notation, and identify properties preserved under rigid motions.

Lesson Overview

Students progress from identifying rigid motions by their properties to applying transformation rules on the coordinate plane, building from single translations to composite transformations. Each task changes exactly one variable to develop fluency with HSG-CO standards.

Materials

  • Vertical whiteboards or large chart paper
  • Dry-erase markers (multiple colors)
  • Pencils and plain paper for notes

Scaffolded Task Progression

1Task 1
Triangle has vertices , , .

Apply the translation rule to find the coordinates of P', Q', and R'.

Draw both triangles on the coordinate plane and label all six vertices.

[ Interactive graph / diagram, available in the full lesson ]
2Task 2
Triangle has vertices , , . (Same triangle as Task 1.)

This time, apply the translation rule .

Find P', Q', R' and draw both triangles. What direction did the triangle move compared to Task 1?

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