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Coordinate Geometry and Transformations Checkpoint

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

This checkpoint reviews transformations, dilations, distance, midpoint, circle equations, and slope evidence. Students need to connect diagrams, coordinates, and algebraic evidence in one mixed set. 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: Geometry assessments mix diagram reading, formulas, coordinates, proof logic, and context so students practice choosing evidence rather than memorizing a single cue.

Worked example

Problem. Worked example from Transformations on the Coordinate Plane: Translate (2, 5) right 3 and down 4.

  1. Add 3 to x and subtract 4 from y.
  2. Connect the result back to Coordinate Geometry and Transformations Checkpoint so the geometric relationship is explicit.
  3. Check the result against the original diagram, units, or proof statement.
  4. Check the result against the original diagram, units, or proof statement.

Answer: (5, 1)

Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.

Practice problems

1. Coordinate Geometry and Transformations Checkpoint review case A from Transformations on the Coordinate Plane: 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. Coordinate Geometry and Transformations Checkpoint review case B from Transformations on the Coordinate Plane: 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. Coordinate Geometry and Transformations Checkpoint review case C from Transformations on the Coordinate Plane: 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. Coordinate Geometry and Transformations Checkpoint review case D from Transformations on the Coordinate Plane: 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. Coordinate Geometry and Transformations Checkpoint review case E from Transformations on the Coordinate Plane: 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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