Translate P(1,2) by ⟨5,-1⟩.
Unit 02 · Lesson 02 · Transformations, Symmetry & Congruence
Reflections Across Axes and Lines
Represent motion with coordinate rules and use preserved distances and angles to reason about congruence and symmetry.
Learning intention
Use accurate diagrams, definitions, measurements, and reasoning to represent motion with coordinate rules and use preserved distances and angles to reason about congruence and symmetry.
Success evidence
- Label the figure and units before calculating.
- Select and justify the governing definition, theorem, relationship, or construction.
- Show enough work that another learner can audit the conclusion.
- Check the result against the diagram, scale, and stated constraints.
Visual model
Represent motion with coordinate rules and use preserved distances and angles to reason about congruence and symmetry.
T_{\langle a,b\rangle}(x,y)=(x+a,y+b)R_{90^\circ}(x,y)=(-y,x)r_{y=x}(x,y)=(y,x)
Worked reasoning
Process: Apply the coordinate rule to each vertex, list the image coordinates, then verify preserved lengths or angles.
- Read the figure and rewrite all given information with correct notation.
- Identify the exact relationship that connects the known and unknown quantities.
- Substitute, construct, or prove one justified step at a time.
- State the result with units and a sentence explaining what it means.
Misconception check: A transformation rule must be applied to every vertex in the same order; changing only part of a figure does not create its image.
Khaemenes Academy · Open-Age Geometry
Reflections Across Axes and Lines
Find, construct, prove, or explain each result. Show reasoning and label units.
Name
Date
Reflect Q(1,2) across the x-axis.
Rotate R(1,2) 90° counterclockwise about the origin.
Which measurements are preserved by every rigid motion?
What is the order of rotational symmetry of a regular hexagon?
Why does the order of transformations matter in a composition?