Reflection: Lines of Reflection, Invariant Points and the Mirror Line

Reflect simple shapes or points in the x-axis, y-axis, and lines such as $x=a$ or $y=b$, reading coordinates off a grid.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • GM4-8
New NZC (2026)
  • NZC26-P4-GEO-SPR-K-Y9-01
  • NZC26-P4-GEO-SPR-P-Y9-02

Resources

Terminology

  • reflection
  • line of reflection
  • mirror line
  • invariant point
  • oblique line
  • image
  • object

Task goals

  • Reflect a shape or point in the x-axis, y-axis, or a line such as x = a or y = b, reading the image coordinates off a grid.
  • Reflect a shape or point in an oblique line, including y = x and y = -x.
  • Identify which points, if any, remain unchanged (invariant) under a given reflection.
  • Given an object and its image, determine and state the equation of the line of reflection, including for less common oblique mirror lines.

Where this fits

What leads into this objective, and where it goes next.

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Reflection: Lines of Reflection, Invariant Points and the Mirror Line

Reflection: Lines of Reflection, Invariant Points and the Mirror Line

Know

A set of points in a plane can be transformed by translation, reflection about a line, and rotation about a fixed point.

Statement▸
Year 9 · Geometry · Spatial reasoning
NZC26-P4-GEO-SPR-K-Y9-01
Do

Transforming 2D shapes in the coordinate plane by translation, reflection about a given line of symmetry, and rotation about a given point by a multiple of 90 degrees

Statement▸
Year 9 · Geometry · Spatial reasoning
NZC26-P4-GEO-SPR-P-Y9-02

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