CMClearMathAcademy

Transformations on the Coordinate Plane

A free Geometry lesson from the “Coordinate Geometry and Proof” unit, with a worked example and practice problems including step-by-step solutions.

Transformations move figures while preserving or changing their position. Translations slide, reflections flip, and rotations turn around a point. In Coordinate Geometry and Proof, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.

What you'll learn

Why it matters: Animators and game developers use translations, reflections, and rotations to move objects predictably on screen.

Worked example

Problem. Reflect (4, -7) across the x-axis.

  1. A reflection across the x-axis keeps x the same.
  2. The y-coordinate changes sign.
  3. (4, -7) becomes (4, 7).
  4. Connect the result back to Transformations on the Coordinate Plane so the geometric relationship is explicit.

Answer: (4, 7)

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.

Practice problems

1. Translate (2, 5) right 3 and down 4.

Choices: (5, 1) · (-1, 9) · (5, 9) · (-1, 1)

Show solution
  1. Add 3 to x and subtract 4 from y.

Answer: (5, 1)

2. Reflect (-3, 8) across the x-axis.

Choices: (-3, -8) · (3, 8) · (3, -8) · (-8, -3)

Show solution
  1. Keep x, change y's sign.

Answer: (-3, -8)

3. Reflect (-6, -2) across the y-axis.

Choices: (6, -2) · (-6, 2) · (6, 2) · (-2, -6)

Show solution
  1. Change x's sign, keep y.

Answer: (6, -2)

4. Rotate (4, 1) 180 degrees about the origin.

Choices: (-4, -1) · (-1, 4) · (1, -4) · (4, -1)

Show solution
  1. A 180-degree rotation changes both signs.

Answer: (-4, -1)

5. Which transformation preserves size and shape?

Choices: Reflection · Dilation by 2 · Stretch only x · Changing one side

Show solution
  1. Reflections are rigid motions.

Answer: Reflection

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